Pub Date : 2026-01-08DOI: 10.1016/j.matcom.2026.01.006
Bushra Aqil , Rakib Mustafa , Ghulam Mustafa
In real-world problems, acquiring precise information can be challenging, as data points often exhibit vagueness, imprecision, or uncertainty. Dealing with uncertain data, which involves intricate processes due to incomplete information, poses difficulties. This paper presents a spherical fuzzy Bézier curve () model for computer-aided geometric design (CAGD) to tackle uncertain data, especially in the context of vehicle lane-changing trajectories. Unlike existing methods that assume exact data and overlook obstacles or uncertainty, employs spherical fuzzy point relations and control point relations are defined using fuzzy set theory to achieve superior uncertainty modeling and adaptability. An , illustrated in a lane-changing scenario, produces adaptive, obstacle-avoiding trajectories that outperform crisp Bézier models. Visualization of spherical fuzzy Bézier surfaces () is also provided in this paper. The de Casteljau algorithm efficiently calculates curve points, and a dynamic method for trajectory planning improves adaptability. This model demonstrates superior performance compared to traditional crisp Bézier methods, providing valuable solutions for automotive design, 3D modeling, and animation.
{"title":"Spherical fuzzy Bézier curve approximation for efficient lane-changing trajectories under uncertain data","authors":"Bushra Aqil , Rakib Mustafa , Ghulam Mustafa","doi":"10.1016/j.matcom.2026.01.006","DOIUrl":"10.1016/j.matcom.2026.01.006","url":null,"abstract":"<div><div>In real-world problems, acquiring precise information can be challenging, as data points often exhibit vagueness, imprecision, or uncertainty. Dealing with uncertain data, which involves intricate processes due to incomplete information, poses difficulties. This paper presents a spherical fuzzy Bézier curve (<span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>f</mi></mrow></msub><mi>BC</mi></mrow></math></span>) model for computer-aided geometric design (CAGD) to tackle uncertain data, especially in the context of vehicle lane-changing trajectories. Unlike existing methods that assume exact data and overlook obstacles or uncertainty, <span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>f</mi></mrow></msub><mi>BC</mi></mrow></math></span> employs spherical fuzzy point relations and control point relations are defined using fuzzy set theory to achieve superior uncertainty modeling and adaptability. An <span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>f</mi></mrow></msub><mi>BC</mi></mrow></math></span>, illustrated in a lane-changing scenario, produces adaptive, obstacle-avoiding trajectories that outperform crisp Bézier models. Visualization of spherical fuzzy Bézier surfaces (<span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>f</mi></mrow></msub><mi>BS</mi></mrow></math></span>) is also provided in this paper. The de Casteljau algorithm efficiently calculates curve points, and a dynamic method for trajectory planning improves adaptability. This model demonstrates superior performance compared to traditional crisp Bézier methods, providing valuable solutions for automotive design, 3D modeling, and animation.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 65-78"},"PeriodicalIF":4.4,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980287","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 : 2026-01-08DOI: 10.1016/j.matcom.2026.01.004
Xiao Guo , Chengzhi Liu
This paper presents a framework for optimizing B-spline knot placement in curve fitting. We show that the perturbation introduced during knot removal increases with the magnitude of the derivative jumps at the removed knots. Based on this observation, we employ polynomial trend filtering to detect abrupt changes in the higher-order discrete derivatives of the sample data, which in turn guides effective knot selection. The proposed framework consists of two main steps: (1) Starting from a densely placed initial knot vector, we optimize the coefficients of the 0-degree B-splines using a generalized lasso model. Knots corresponding to significant changes in discrete derivatives of a selected order are identified as active; (2) A higher-order B-spline approximation is then constructed using these active knots. Redundant knots are iteratively removed while maintaining the approximation quality. We validate the method on several functions and parameter curve fitting tasks. Results show that the proposed approach yields B-spline approximations with a similar number of knots as existing methods, while achieving comparable or improved accuracy.
{"title":"Two-step optimization of knots in B-spline curve approximation","authors":"Xiao Guo , Chengzhi Liu","doi":"10.1016/j.matcom.2026.01.004","DOIUrl":"10.1016/j.matcom.2026.01.004","url":null,"abstract":"<div><div>This paper presents a framework for optimizing B-spline knot placement in curve fitting. We show that the perturbation introduced during knot removal increases with the magnitude of the derivative jumps at the removed knots. Based on this observation, we employ polynomial trend filtering to detect abrupt changes in the higher-order discrete derivatives of the sample data, which in turn guides effective knot selection. The proposed framework consists of two main steps: (1) Starting from a densely placed initial knot vector, we optimize the coefficients of the 0-degree B-splines using a generalized lasso model. Knots corresponding to significant changes in discrete derivatives of a selected order are identified as active; (2) A higher-order B-spline approximation is then constructed using these active knots. Redundant knots are iteratively removed while maintaining the approximation quality. We validate the method on several functions and parameter curve fitting tasks. Results show that the proposed approach yields B-spline approximations with a similar number of knots as existing methods, while achieving comparable or improved accuracy.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 53-64"},"PeriodicalIF":4.4,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929184","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 : 2026-01-06DOI: 10.1016/j.matcom.2026.01.003
Hiroyuki Sato , Yuya Yamakawa , Kensuke Aihara
For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Riemannian version of the Armijo line search for global convergence. Such existing methods need to compute the value of a retraction mapping regarding the search direction several times at each iteration; this may result in high computational costs, particularly if computing the value of the retraction is expensive. To address this issue, this study focuses on embedded Riemannian submanifolds of the Euclidean spaces and proposes a novel Riemannian line search that achieves lower computational cost by incorporating a new strategy that computes the retraction only when inevitable. A class of Riemannian optimization algorithms, including the steepest descent and Newton methods, with the new line search strategy is proposed and proved to be globally convergent. Furthermore, numerical experiments on solving optimization problems on several types of embedded Riemannian submanifolds illustrate that the proposed methods are superior to the standard Riemannian Armijo line search-based methods.
{"title":"Modified Armijo line search in optimization on Riemannian submanifolds with reduced computational cost","authors":"Hiroyuki Sato , Yuya Yamakawa , Kensuke Aihara","doi":"10.1016/j.matcom.2026.01.003","DOIUrl":"10.1016/j.matcom.2026.01.003","url":null,"abstract":"<div><div>For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Riemannian version of the Armijo line search for global convergence. Such existing methods need to compute the value of a retraction mapping regarding the search direction several times at each iteration; this may result in high computational costs, particularly if computing the value of the retraction is expensive. To address this issue, this study focuses on embedded Riemannian submanifolds of the Euclidean spaces and proposes a novel Riemannian line search that achieves lower computational cost by incorporating a new strategy that computes the retraction only when inevitable. A class of Riemannian optimization algorithms, including the steepest descent and Newton methods, with the new line search strategy is proposed and proved to be globally convergent. Furthermore, numerical experiments on solving optimization problems on several types of embedded Riemannian submanifolds illustrate that the proposed methods are superior to the standard Riemannian Armijo line search-based methods.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 260-274"},"PeriodicalIF":4.4,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038828","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 : 2026-01-06DOI: 10.1016/j.matcom.2026.01.001
Ning Xu , Li Tang , Abdullah A. Al-Barakati
This paper addresses the fixed-time optimal bipartite containment control problem for nonlinear multi-agent systems under multiple simultaneous faults — including concurrent actuator and sensor faults — and input saturation. A key contribution is a unified disturbance-observer–based reinforcement learning framework that integrates fault tolerance with optimal control objectives. By designing a novel performance index function, the traditional containment control problem is reformulated as an optimal control problem, enabling an explicit trade-off between control accuracy and energy consumption. To solve the corresponding Hamilton–Jacobi–Bellman equation without relying on accurate system dynamics, a neural reinforcement learning algorithm with an identifier–critic–actor architecture is developed. A disturbance observer is incorporated to actively estimate and compensate for external disturbances, while an auxiliary system is introduced to alleviate input saturation effects. The resulting fixed-time optimal controller ensures that all bipartite containment errors converge to a small neighborhood of the origin within a fixed time independent of initial conditions, while maintaining uniform boundedness of all closed-loop signals. Simulation results validate the effectiveness and superiority of the proposed method in achieving simultaneous fault tolerance, disturbance rejection, and optimal performance under saturated actuation conditions.
{"title":"Fixed-time optimal bipartite containment fault-tolerant control for multi-agent systems under multiple faults and saturated actuation","authors":"Ning Xu , Li Tang , Abdullah A. Al-Barakati","doi":"10.1016/j.matcom.2026.01.001","DOIUrl":"10.1016/j.matcom.2026.01.001","url":null,"abstract":"<div><div>This paper addresses the fixed-time optimal bipartite containment control problem for nonlinear multi-agent systems under multiple simultaneous faults — including concurrent actuator and sensor faults — and input saturation. A key contribution is a unified disturbance-observer–based reinforcement learning framework that integrates fault tolerance with optimal control objectives. By designing a novel performance index function, the traditional containment control problem is reformulated as an optimal control problem, enabling an explicit trade-off between control accuracy and energy consumption. To solve the corresponding Hamilton–Jacobi–Bellman equation without relying on accurate system dynamics, a neural reinforcement learning algorithm with an identifier–critic–actor architecture is developed. A disturbance observer is incorporated to actively estimate and compensate for external disturbances, while an auxiliary system is introduced to alleviate input saturation effects. The resulting fixed-time optimal controller ensures that all bipartite containment errors converge to a small neighborhood of the origin within a fixed time independent of initial conditions, while maintaining uniform boundedness of all closed-loop signals. Simulation results validate the effectiveness and superiority of the proposed method in achieving simultaneous fault tolerance, disturbance rejection, and optimal performance under saturated actuation conditions.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 242-259"},"PeriodicalIF":4.4,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038832","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 : 2026-01-05DOI: 10.1016/j.matcom.2025.12.021
Quen-Yi Lin, Ming-Cheng Shiue
Spectral deferred correction (SDC) methods constitute a class of numerical schemes that achieve arbitrarily high-order accuracy by iteratively applying a low-order method. These methods combine high accuracy with low computational cost, making them attractive for numerically solving differential equations. In this paper, the explicit two-grid SDC method for the generalized multi-order fractional differential equations and its theoretical analysis are studied. The analysis demonstrates that the proposed scheme is stable, provided that the time step size is sufficiently small, and that it achieves high-order convergence under the same condition. Numerical experiments are provided to validate and illustrate the theoretical findings.
{"title":"A two-grid spectral deferred correction method for the generalized multi-order fractional differential equations","authors":"Quen-Yi Lin, Ming-Cheng Shiue","doi":"10.1016/j.matcom.2025.12.021","DOIUrl":"10.1016/j.matcom.2025.12.021","url":null,"abstract":"<div><div>Spectral deferred correction (SDC) methods constitute a class of numerical schemes that achieve arbitrarily high-order accuracy by iteratively applying a low-order method. These methods combine high accuracy with low computational cost, making them attractive for numerically solving differential equations. In this paper, the explicit two-grid SDC method for the generalized multi-order fractional differential equations and its theoretical analysis are studied. The analysis demonstrates that the proposed scheme is stable, provided that the time step size is sufficiently small, and that it achieves high-order convergence under the same condition. Numerical experiments are provided to validate and illustrate the theoretical findings.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 1-20"},"PeriodicalIF":4.4,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145904148","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 : 2026-01-05DOI: 10.1016/S0378-4754(25)00563-4
{"title":"IMACS Calendar of Events","authors":"","doi":"10.1016/S0378-4754(25)00563-4","DOIUrl":"10.1016/S0378-4754(25)00563-4","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Page 525"},"PeriodicalIF":4.4,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145924836","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 : 2026-01-05DOI: 10.1016/S0378-4754(25)00562-2
{"title":"News of IMACS","authors":"","doi":"10.1016/S0378-4754(25)00562-2","DOIUrl":"10.1016/S0378-4754(25)00562-2","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Page 524"},"PeriodicalIF":4.4,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145924835","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 : 2026-01-03DOI: 10.1016/j.matcom.2025.12.022
Muhammad Amin S. Murad , Usman Younas , Homan Emadifar , Mujahid Iqbal , Wael W. Mohammed , Karim K. Ahmed
In this paper, we employ the modified generalized Riccati equation approach to derive a variety of exact solutions for the Ivancevic option pricing model incorporating the conformable derivative. The Ivancevic option pricing equation is structured using an adaptive nonlinear Schrödinger equation, which describes the option-pricing wave function based on time and stock price. This equation captures the typical regulated Brownian motion seen in financial markets. The predictive nature of the model allows financial analysts to forecast option prices under varying market conditions. The model helps traders to price complex options with greater accuracy by considering nonlinear market dynamics. A variety of soliton solutions to the conformable Ivancevic model are derived, including dark, mixed dark–bright, singular, bell-shaped, and wave solutions. To provide deeper insights into their dynamical properties and physical significance, these solutions are visualized through three-dimensional plots, two-dimensional plots, and contour plots. The graphical representations underscore the intricate dynamics and potential financial applications of soliton solutions within the conformable framework, demonstrating their relevance in option pricing theory and nonlinear financial modeling.
{"title":"Diverse soliton solutions to the conformable Ivancevic option pricing model via the modified generalized Riccati equation mapping method","authors":"Muhammad Amin S. Murad , Usman Younas , Homan Emadifar , Mujahid Iqbal , Wael W. Mohammed , Karim K. Ahmed","doi":"10.1016/j.matcom.2025.12.022","DOIUrl":"10.1016/j.matcom.2025.12.022","url":null,"abstract":"<div><div>In this paper, we employ the modified generalized Riccati equation approach to derive a variety of exact solutions for the Ivancevic option pricing model incorporating the conformable derivative. The Ivancevic option pricing equation is structured using an adaptive nonlinear Schrödinger equation, which describes the option-pricing wave function based on time and stock price. This equation captures the typical regulated Brownian motion seen in financial markets. The predictive nature of the model allows financial analysts to forecast option prices under varying market conditions. The model helps traders to price complex options with greater accuracy by considering nonlinear market dynamics. A variety of soliton solutions to the conformable Ivancevic model are derived, including dark, mixed dark–bright, singular, bell-shaped, and wave solutions. To provide deeper insights into their dynamical properties and physical significance, these solutions are visualized through three-dimensional plots, two-dimensional plots, and contour plots. The graphical representations underscore the intricate dynamics and potential financial applications of soliton solutions within the conformable framework, demonstrating their relevance in option pricing theory and nonlinear financial modeling.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"244 ","pages":"Pages 213-225"},"PeriodicalIF":4.4,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927610","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 : 2026-01-03DOI: 10.1016/j.matcom.2025.12.023
Samuel Asante Gyamerah , Emmanuel Afrifa , Perpetual Andam Boiquaye , Nelson Dzupire
Bank runs can destabilize individual institutions and, through financial networks, spread into general economic crises. The study explores the interconnection of systemic risk in the banking system, emphasizing interbank networks as the primary means of propagating financial contagion. We propose a compartmental system through which contagion is propagated. The system classifies the banks in the network into six compartments (undistressed, exposed, distressed, liquid, run, and failed states). We capture the dynamics of distress transmission through interbank interactions and depositor behaviours. We derive the basic reproduction number to characterize the threshold conditions for systemic stability and identify both risk-free and risk-persistent equilibrium points. Through sensitivity experiments, we identify the parameters that exert the strongest influence on contagion dynamics—the contact rate between banks, the level of behavioural compliance, and transition intensities. Building on these insights, we formulate an optimal-control framework that incorporates three forms of intervention: deposit-insurance protection, policies aimed at calming depositors, and targeted liquidity intervention. Using Pontryagin’s Maximum Principle, we derive the time paths of these interventions that jointly reduce the spread of distress while keeping regulatory costs manageable. The numerical results highlight the importance of acting early: even a moderate level of deposit-insurance coverage, when implemented at the right moment, substantially dampens the transmission of shocks across the network. The study offers practical guidance for the design of policy tools intended to contain systemic risk in interconnected banking systems.
{"title":"Modelling financial contagion and optimal policy design for bank runs and systemic risk","authors":"Samuel Asante Gyamerah , Emmanuel Afrifa , Perpetual Andam Boiquaye , Nelson Dzupire","doi":"10.1016/j.matcom.2025.12.023","DOIUrl":"10.1016/j.matcom.2025.12.023","url":null,"abstract":"<div><div>Bank runs can destabilize individual institutions and, through financial networks, spread into general economic crises. The study explores the interconnection of systemic risk in the banking system, emphasizing interbank networks as the primary means of propagating financial contagion. We propose a compartmental system through which contagion is propagated. The system classifies the banks in the network into six compartments (undistressed, exposed, distressed, liquid, run, and failed states). We capture the dynamics of distress transmission through interbank interactions and depositor behaviours. We derive the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> to characterize the threshold conditions for systemic stability and identify both risk-free and risk-persistent equilibrium points. Through sensitivity experiments, we identify the parameters that exert the strongest influence on contagion dynamics—the contact rate between banks, the level of behavioural compliance, and transition intensities. Building on these insights, we formulate an optimal-control framework that incorporates three forms of intervention: deposit-insurance protection, policies aimed at calming depositors, and targeted liquidity intervention. Using Pontryagin’s Maximum Principle, we derive the time paths of these interventions that jointly reduce the spread of distress while keeping regulatory costs manageable. The numerical results highlight the importance of acting early: even a moderate level of deposit-insurance coverage, when implemented at the right moment, substantially dampens the transmission of shocks across the network. The study offers practical guidance for the design of policy tools intended to contain systemic risk in interconnected banking systems.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 35-52"},"PeriodicalIF":4.4,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929178","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 : 2025-12-31DOI: 10.1016/j.matcom.2025.12.019
Lin Zhu , Rumin Dong , Qin Sheng
This paper investigates the properties of discrete variable approximations for the quenching solutions of a nonlinear one-dimensional dual Riemann–Liouville fractional-order problem. The fractional-order spatial derivatives are discretized using a weighted average approach, combined with both the standard and shifted Grünwald formulas. The advection term is approximated via a direct Euler scheme, resulting in a semi-discretized system of nonlinear, constant-coefficient equations. The robustness of the proposed discrete variable method is demonstrated and validated through rigorous mathematical analysis and numerical experiments. The study systematically examines the effects of the critical length, convective terms, and the two fractional orders on the quenching phenomenon. Detailed computational results and analyses provide a deeper understanding of quenching behavior in nonlinear fractional-order problems.
{"title":"A semi-adaptive discrete variable method for emulating dual space fractional convection–diffusion quenching problems","authors":"Lin Zhu , Rumin Dong , Qin Sheng","doi":"10.1016/j.matcom.2025.12.019","DOIUrl":"10.1016/j.matcom.2025.12.019","url":null,"abstract":"<div><div>This paper investigates the properties of discrete variable approximations for the quenching solutions of a nonlinear one-dimensional dual Riemann–Liouville fractional-order problem. The fractional-order spatial derivatives are discretized using a weighted average approach, combined with both the standard and shifted Grünwald formulas. The advection term is approximated via a direct Euler scheme, resulting in a semi-discretized system of nonlinear, constant-coefficient equations. The robustness of the proposed discrete variable method is demonstrated and validated through rigorous mathematical analysis and numerical experiments. The study systematically examines the effects of the critical length, convective terms, and the two fractional orders on the quenching phenomenon. Detailed computational results and analyses provide a deeper understanding of quenching behavior in nonlinear fractional-order problems.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"244 ","pages":"Pages 196-212"},"PeriodicalIF":4.4,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927490","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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