Pub Date : 2026-10-01Epub Date: 2026-01-27DOI: 10.1016/j.nonrwa.2026.104606
Chun Wu
This paper deals with the following quasilinear chemotaxis systemunder the homogeneous Neumann boundary condition in with smooth boundary ∂Ω, where the parameters a, b > 0 and m > 1. It is shown that there is at least one global weak solution for the system being discussed.
{"title":"Global existence of weak solutions to a quasilinear parabolic chemotaxis system","authors":"Chun Wu","doi":"10.1016/j.nonrwa.2026.104606","DOIUrl":"10.1016/j.nonrwa.2026.104606","url":null,"abstract":"<div><div>This paper deals with the following quasilinear chemotaxis system<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>=</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>∇</mi><msup><mi>u</mi><mi>m</mi></msup><mo>−</mo><mi>u</mi><mi>v</mi><mi>∇</mi><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>a</mi><mi>u</mi><mo>−</mo><mi>b</mi><msup><mi>u</mi><mn>2</mn></msup><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>v</mi><mi>t</mi></msub><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>v</mi><mo>−</mo><mi>u</mi><mi>v</mi><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mtd></mtr></mtable></mrow></math></span></span></span>under the homogeneous Neumann boundary condition in <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><msup><mi>R</mi><mi>n</mi></msup><mspace></mspace><mspace></mspace><mrow><mo>(</mo><mi>n</mi><mo>≥</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> with smooth boundary ∂Ω, where the parameters <em>a, b</em> > 0 and <em>m</em> > 1. It is shown that there is at least one global weak solution for the system being discussed.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104606"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146077472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-02-08DOI: 10.1016/j.cam.2026.117417
Sana Jabeen , Muhammad , Masood Khan , Syed Modassir Hussain
Artificial intelligence (AI), a revolutionary force in modern scientific research across various domains, has the potential to provide new solutions for highly complex and challenging physical models. This paper investigates the incompressible flow of an Eyring-Powell magneto-nanofluid model (EPMNM) over a stretching surface. The effects of thermal and solutal mechanisms are analyzed by incorporating variable thermal conductivity, mass diffusivity, chemical reactions, and heat sources. The Buongiorno model is employed to capture the influence of nanofluids through thermophoresis and Brownian motion. The relevant transformations convert the governing PDEs into coupled nonlinear ODEs. The numerical solution is obtained using the fourth-order Runge-Kutta-Fehlberg method in conjunction with the shooting technique. Furthermore, the Levenberg-Marquardt Neural Network Algorithm (LMNNA) is employed in an intelligent, ANN-based numerically validated solver to analyze the resulting fluid model. The BVP4C approach generated a chart displaying the behavior of the friction drag, Local Motile Density Number (LMDN), thermal, and solutal transportation rates. A dataset for various scenarios of the intriguing and comprehensive nanofluid model has been produced by exploiting BVP4C. The strengths of the machine learning analysis using LMNNA are then investigated through physical quantities such as SFC, LNN, LSHN, and LMDN. Datasets comprising 60 and 45 outcomes are categorized into three groups: training (70%), validation (15%), and testing (15%). The hidden layer consists of ten neurons. Tables 4 through 7 present the ANN predictions alongside the numerical values for SFC, LNN, LSHN, and LMDN. The accuracy of the developed neural network for these physical quantities is assessed using regression analysis and mean squared error.
{"title":"Machine learning analysis of thermal and solutal transport rates for Eyring-Powell magneto-nanomaterial model (EPMNM)","authors":"Sana Jabeen , Muhammad , Masood Khan , Syed Modassir Hussain","doi":"10.1016/j.cam.2026.117417","DOIUrl":"10.1016/j.cam.2026.117417","url":null,"abstract":"<div><div>Artificial intelligence (AI), a revolutionary force in modern scientific research across various domains, has the potential to provide new solutions for highly complex and challenging physical models. This paper investigates the incompressible flow of an Eyring-Powell magneto-nanofluid model (EPMNM) over a stretching surface. The effects of thermal and solutal mechanisms are analyzed by incorporating variable thermal conductivity, mass diffusivity, chemical reactions, and heat sources. The Buongiorno model is employed to capture the influence of nanofluids through thermophoresis and Brownian motion. The relevant transformations convert the governing PDEs into coupled nonlinear ODEs. The numerical solution is obtained using the fourth-order Runge-Kutta-Fehlberg method in conjunction with the shooting technique. Furthermore, the Levenberg-Marquardt Neural Network Algorithm (LMNNA) is employed in an intelligent, ANN-based numerically validated solver to analyze the resulting fluid model. The BVP4C approach generated a chart displaying the behavior of the friction drag, Local Motile Density Number (LMDN), thermal, and solutal transportation rates. A dataset for various scenarios of the intriguing and comprehensive nanofluid model has been produced by exploiting BVP4C. The strengths of the machine learning analysis using LMNNA are then investigated through physical quantities such as SFC, LNN, LSHN, and LMDN. Datasets comprising 60 and 45 outcomes are categorized into three groups: training (70%), validation (15%), and testing (15%). The hidden layer consists of ten neurons. Tables 4 through 7 present the ANN predictions alongside the numerical values for SFC, LNN, LSHN, and LMDN. The accuracy of the developed neural network for these physical quantities is assessed using regression analysis and mean squared error.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117417"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-02-14DOI: 10.1016/j.cam.2026.117455
Lakhlifa Sadek , Hamad Talibi Alaoui , Ahmad Sami Bataineh , Ishak Hashim
This study addresses the numerical solution of large-scale linear systems of fractional differential equations (LSFDEs) featuring a low-rank constant term a class of problems not previously investigated in the literature. We propose two novel numerical approaches for solving such systems. The first method exploits the integral representation of the exact solution and employs a Krylov-based approximation to compute the action of the matrix Mittag–Leffler function on a block of vectors. The second approach projects the original high-dimensional fractional system onto an extended block Krylov subspace, reducing it to a significantly smaller fractional differential system. This reduced system is then solved using either a tailored implementation of the Grünwald-Letnikov scheme or a fractional backward differentiation formula, both adapted to the projected setting. The resulting low-rank approximate solution is iteratively refined by expanding the projection subspace until a prescribed tolerance is achieved. We derive explicit expressions for the residual and error norms and establish associated convergence estimates. To validate the computational efficiency and accuracy of the proposed methods, we conduct extensive numerical experiments on several benchmark problems. The results demonstrate that our approaches substantially reduce computational time while maintaining high numerical precision, outperforming existing conventional solvers for large-scale fractional systems.
{"title":"Extended block Krylov subspace approaches for solving large-scale linear system of fractional DEs","authors":"Lakhlifa Sadek , Hamad Talibi Alaoui , Ahmad Sami Bataineh , Ishak Hashim","doi":"10.1016/j.cam.2026.117455","DOIUrl":"10.1016/j.cam.2026.117455","url":null,"abstract":"<div><div>This study addresses the numerical solution of large-scale linear systems of fractional differential equations (LSFDEs) featuring a low-rank constant term a class of problems not previously investigated in the literature. We propose two novel numerical approaches for solving such systems. The first method exploits the integral representation of the exact solution and employs a Krylov-based approximation to compute the action of the matrix Mittag–Leffler function on a block of vectors. The second approach projects the original high-dimensional fractional system onto an extended block Krylov subspace, reducing it to a significantly smaller fractional differential system. This reduced system is then solved using either a tailored implementation of the Grünwald-Letnikov scheme or a fractional backward differentiation formula, both adapted to the projected setting. The resulting low-rank approximate solution is iteratively refined by expanding the projection subspace until a prescribed tolerance is achieved. We derive explicit expressions for the residual and error norms and establish associated convergence estimates. To validate the computational efficiency and accuracy of the proposed methods, we conduct extensive numerical experiments on several benchmark problems. The results demonstrate that our approaches substantially reduce computational time while maintaining high numerical precision, outperforming existing conventional solvers for large-scale fractional systems.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117455"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-02-17DOI: 10.1016/j.cam.2026.117451
Doulaye Dembélé
The singular value decomposition (SVD) allows to write a matrix as a product of a left singular vectors matrix, a nonnegative singular values diagonal matrix and a right singular vectors matrix. Among the applications of the SVD are the principal component analysis, the low-rank matrix approximation and the solving of a linear system of equations. The methods used for computing this decomposition allow to get the complete or partial result. For very large size matrix, the probabilistic methods allow to get partial result by using less computational load. A power method is proposed in this paper for computing all or the k first largest SVD subspaces for a real-valued matrix. The k first right singular vectors of this method are the k columns of a neural network encoder weight matrix. The accuracy of this iterative search method depends on the behavior of the singular values and the settings of the gradient search optimizer used. A R package implementing the proposed method is available at https://cran.r-project.org/web/packages/psvd/index.html.
{"title":"A power method for computing singular value decomposition","authors":"Doulaye Dembélé","doi":"10.1016/j.cam.2026.117451","DOIUrl":"10.1016/j.cam.2026.117451","url":null,"abstract":"<div><div>The singular value decomposition (SVD) allows to write a matrix as a product of a left singular vectors matrix, a nonnegative singular values diagonal matrix and a right singular vectors matrix. Among the applications of the SVD are the principal component analysis, the low-rank matrix approximation and the solving of a linear system of equations. The methods used for computing this decomposition allow to get the complete or partial result. For very large size matrix, the probabilistic methods allow to get partial result by using less computational load. A power method is proposed in this paper for computing all or the <em>k</em> first largest SVD subspaces for a real-valued matrix. The <em>k</em> first right singular vectors of this method are the <em>k</em> columns of a neural network encoder weight matrix. The accuracy of this iterative search method depends on the behavior of the singular values and the settings of the gradient search optimizer used. A R package implementing the proposed method is available at <span><span>https://cran.r-project.org/web/packages/psvd/index.html</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117451"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-02-26DOI: 10.1016/j.cam.2026.117495
Minsheng Huang , Ruo Li , Kai Yan , Chengbao Yao , Wenjun Ying
The reference field method, known as the difference formulation, is a key variance reduction technique for Monte Carlo simulations of thermal radiation transport problems. When the material temperature is relatively high and the spatial temperature gradient is moderate, this method demonstrates significant advantages in reducing variance compared to classical Monte Carlo methods. However, in problems with larger temperature gradients, this method has not only been found ineffective at reducing statistical noise, but in some cases, it even increases noise compared to classical Monte Carlo methods. The global optimal reference field method, a recently proposed variance reduction technique, effectively reduces the average energy weight of Monte Carlo particles, thereby decreasing variance. Its effectiveness has been validated both theoretically and numerically, demonstrating a significant reduction in statistical errors for problems with large temperature gradients. In our previous work, instead of computing the exact global optimal reference field, we developed an approximate, physically motivated method to find a relatively better reference field using a selection scheme. In this work, we reformulate the problem of determining the global optimal reference field as a linear programming problem and solve it exactly. To further enhance computational efficiency, we use the MindOpt solver, which leverages graph neural network methods. Numerical experiments demonstrate that the MindOpt solver not only solves linear programming problems accurately but also significantly outperforms the Simplex and interior-point methods in terms of computational efficiency. The global optimal reference field method combined with the MindOpt solver not only improves computational efficiency but also substantially reduces statistical errors.
{"title":"An efficient Monte Carlo simulation for radiation transport based on global optimal reference field","authors":"Minsheng Huang , Ruo Li , Kai Yan , Chengbao Yao , Wenjun Ying","doi":"10.1016/j.cam.2026.117495","DOIUrl":"10.1016/j.cam.2026.117495","url":null,"abstract":"<div><div>The reference field method, known as the difference formulation, is a key variance reduction technique for Monte Carlo simulations of thermal radiation transport problems. When the material temperature is relatively high and the spatial temperature gradient is moderate, this method demonstrates significant advantages in reducing variance compared to classical Monte Carlo methods. However, in problems with larger temperature gradients, this method has not only been found ineffective at reducing statistical noise, but in some cases, it even increases noise compared to classical Monte Carlo methods. The global optimal reference field method, a recently proposed variance reduction technique, effectively reduces the average energy weight of Monte Carlo particles, thereby decreasing variance. Its effectiveness has been validated both theoretically and numerically, demonstrating a significant reduction in statistical errors for problems with large temperature gradients. In our previous work, instead of computing the exact global optimal reference field, we developed an approximate, physically motivated method to find a relatively better reference field using a selection scheme. In this work, we reformulate the problem of determining the global optimal reference field as a linear programming problem and solve it exactly. To further enhance computational efficiency, we use the MindOpt solver, which leverages graph neural network methods. Numerical experiments demonstrate that the MindOpt solver not only solves linear programming problems accurately but also significantly outperforms the Simplex and interior-point methods in terms of computational efficiency. The global optimal reference field method combined with the MindOpt solver not only improves computational efficiency but also substantially reduces statistical errors.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117495"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-02-21DOI: 10.1016/j.cam.2026.117474
Fangfang Shi , Guoju Ye , Wei Liu , Debdas Ghosh
The main objective of this paper is to investigate the KKT optimality condition for fuzzy optimization problems with inequality constraints. To begin with, by proving that the intersection of the cone of descent directions and the cone of feasible directions at the optimal point is an empty set, we establish the first-order optimality condition for unconstrained fuzzy optimization problems. On this basis, the Fritz-John optimality condition for fuzzy optimization problems with inequality constraints is derived through the fuzzy Gordan’s theorem. Furthermore, in order to ensure that the Lagrangian multipliers must satisfy not all zero, we strengthen the assumptions to deduce the KKT optimality condition. Meanwhile, some numerical examples are created to verify the validity of theoretical results. It is particularly worth mentioning that the optimality conditions established in this paper are such that zero belongs to a certain interval, which makes our results computationally superior than in the previous literature, where the optimality conditions are equalities. Finally, the developed optimality conditions are employed to address a binary classification problem related to support vector machines with fuzzy data.
{"title":"Optimality conditions for fuzzy optimization problems and its application to classification problems with fuzzy data","authors":"Fangfang Shi , Guoju Ye , Wei Liu , Debdas Ghosh","doi":"10.1016/j.cam.2026.117474","DOIUrl":"10.1016/j.cam.2026.117474","url":null,"abstract":"<div><div>The main objective of this paper is to investigate the KKT optimality condition for fuzzy optimization problems with inequality constraints. To begin with, by proving that the intersection of the cone of descent directions and the cone of feasible directions at the optimal point is an empty set, we establish the first-order optimality condition for unconstrained fuzzy optimization problems. On this basis, the Fritz-John optimality condition for fuzzy optimization problems with inequality constraints is derived through the fuzzy Gordan’s theorem. Furthermore, in order to ensure that the Lagrangian multipliers must satisfy not all zero, we strengthen the assumptions to deduce the KKT optimality condition. Meanwhile, some numerical examples are created to verify the validity of theoretical results. It is particularly worth mentioning that the optimality conditions established in this paper are such that zero belongs to a certain interval, which makes our results computationally superior than in the previous literature, where the optimality conditions are equalities. Finally, the developed optimality conditions are employed to address a binary classification problem related to support vector machines with fuzzy data.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117474"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-02-27DOI: 10.1016/j.cam.2026.117492
Xiao Peng , Yijing Wang , Zhiqiang Zuo
This paper explores the asymptotic leader-follower consensus and Mittag-Leffler leader-follower consensus for variable-order multi-agent systems in the presence of unknown nonlinearity and external disturbances. Under the fixed/switching topologies, sufficient consensus criteria are respectively developed by proposing non-switched/switched distributed adaptive neural network-based dynamic event-trigger control schemes. At the end of this paper, some numerical simulations and comparison results are presented to imply the effectiveness of the proposed control strategies.
{"title":"Leader-follower consensus for variable-order multi-agent systems with fixed/switching topologies","authors":"Xiao Peng , Yijing Wang , Zhiqiang Zuo","doi":"10.1016/j.cam.2026.117492","DOIUrl":"10.1016/j.cam.2026.117492","url":null,"abstract":"<div><div>This paper explores the asymptotic leader-follower consensus and Mittag-Leffler leader-follower consensus for variable-order multi-agent systems in the presence of unknown nonlinearity and external disturbances. Under the fixed/switching topologies, sufficient consensus criteria are respectively developed by proposing non-switched/switched distributed adaptive neural network-based dynamic event-trigger control schemes. At the end of this paper, some numerical simulations and comparison results are presented to imply the effectiveness of the proposed control strategies.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117492"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the steepest descent method for unconstrained optimization problems involving quasiconvex fuzzy objective functions under granular differentiability. We introduce a class of granular quasiconvex and pseudoconvex functions, referred to as gr-quasiconvexity and gr-pseudoconvexity. Key properties of these functions and their interrelations are discussed. Leveraging the theory of quasi-Fejr convergence, we prove that the sequence generated by the steepest descent method with a generalized Armijo search converges completely to a granular stationary point of the fuzzy optimization problem. Several numerical examples are provided to demonstrate the effectiveness of the proposed approach. Additionally, a potential application in finance is considered and solved using our method.
{"title":"Steepest descent method with a generalized Armijo search to solve quasiconvex fuzzy optimization problems under granular differentiability","authors":"Shenglan Chen , Li Zhong , Zengbao Wu , Changjie Fang","doi":"10.1016/j.cam.2026.117432","DOIUrl":"10.1016/j.cam.2026.117432","url":null,"abstract":"<div><div>In this paper, we study the steepest descent method for unconstrained optimization problems involving quasiconvex fuzzy objective functions under granular differentiability. We introduce a class of granular quasiconvex and pseudoconvex functions, referred to as <em>gr</em>-quasiconvexity and <em>gr</em>-pseudoconvexity. Key properties of these functions and their interrelations are discussed. Leveraging the theory of quasi-Fej<span><math><mover><mi>e</mi><mo>´</mo></mover></math></span>r convergence, we prove that the sequence generated by the steepest descent method with a generalized Armijo search converges completely to a granular stationary point of the fuzzy optimization problem. Several numerical examples are provided to demonstrate the effectiveness of the proposed approach. Additionally, a potential application in finance is considered and solved using our method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117432"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-02-17DOI: 10.1016/j.cam.2026.117448
Qiumei Huang , Cheng Wang , Gangfan Zhong
In this paper, we propose two multi-step, linearized numerical schemes for a nonlinear convection-diffusion-reaction (CDR) equation with vanishing delay, a temporally nonlocal partial differential equation. These semi-implicit numerical schemes use a combination of explicit Adams–Bashforth extrapolation for the nonlinear term and implicit Adams–Moulton interpolation for the diffusion term. A long stencil finite difference approximation is employed for the spatial discretization, and a boundary extrapolation is used to prescribe the solution at “ghost” points lying outside of the computational domain. The numerical stability and convergence analysis is provided, and the discrete ℓ2 convergence estimate is obtained, with fourth-order spatial accuracy and high-order (third- or fourth-order) temporal accuracy. A few numerical experiments are also presented to confirm the theoretical results.
{"title":"Extended multi-step high-order numerical methods for the nonlinear convection-diffusion-reaction equation with vanishing delay","authors":"Qiumei Huang , Cheng Wang , Gangfan Zhong","doi":"10.1016/j.cam.2026.117448","DOIUrl":"10.1016/j.cam.2026.117448","url":null,"abstract":"<div><div>In this paper, we propose two multi-step, linearized numerical schemes for a nonlinear convection-diffusion-reaction (CDR) equation with vanishing delay, a temporally nonlocal partial differential equation. These semi-implicit numerical schemes use a combination of explicit Adams–Bashforth extrapolation for the nonlinear term and implicit Adams–Moulton interpolation for the diffusion term. A long stencil finite difference approximation is employed for the spatial discretization, and a boundary extrapolation is used to prescribe the solution at “ghost” points lying outside of the computational domain. The numerical stability and convergence analysis is provided, and the discrete ℓ<sup>2</sup> convergence estimate is obtained, with fourth-order spatial accuracy and high-order (third- or fourth-order) temporal accuracy. A few numerical experiments are also presented to confirm the theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117448"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-10-01Epub Date: 2026-02-22DOI: 10.1016/j.cam.2026.117507
Nguyen Song Ha , Simeon Reich , Truong Minh Tuyen , Pham Thi Thu
We study the mixed split feasibility problem in real Hilbert space. In order to find a solution to this problem, we use hybrid and shrinking projection methods to propose two new inertial multistep projection-type algorithms. A distinctive feature of our methods is that the inertial parameters are only required to be bounded, rather than diminishing or constrained to lie within fixed intervals such as or [0, a], as is commonly imposed in many existing inertial schemes. This relaxation makes the selection of inertial factors more flexible and easier to implement while still ensuring strong convergence. In addition, the other control parameters are selected so that the implementation of our algorithm does not depend on any prior information regarding the norms of the transfer operators.
{"title":"Two inertial multistep projection-type algorithms for solving mixed split feasibility problems in Hilbert space","authors":"Nguyen Song Ha , Simeon Reich , Truong Minh Tuyen , Pham Thi Thu","doi":"10.1016/j.cam.2026.117507","DOIUrl":"10.1016/j.cam.2026.117507","url":null,"abstract":"<div><div>We study the mixed split feasibility problem in real Hilbert space. In order to find a solution to this problem, we use hybrid and shrinking projection methods to propose two new inertial multistep projection-type algorithms. A distinctive feature of our methods is that the inertial parameters are only required to be bounded, rather than diminishing or constrained to lie within fixed intervals such as <span><math><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span> or [0, <em>a</em>], as is commonly imposed in many existing inertial schemes. This relaxation makes the selection of inertial factors more flexible and easier to implement while still ensuring strong convergence. In addition, the other control parameters are selected so that the implementation of our algorithm does not depend on any prior information regarding the norms of the transfer operators.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117507"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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