Pub Date : 2026-02-01Epub Date: 2026-03-04DOI: 10.1016/j.rinam.2026.100694
Wei Ma, Yuqing Zhu
In 2021, for inverse singular value problems, a quadratically convergent algorithm (Wei and Chen, 2021) based on matrix multiplication (Ogita and Aishima, 2020) was designed for inverse singular value problems. Although this method has some good features compared to other quadratic convergence methods, it is not suitable for multiple singular values. In this paper, we propose a modified algorithm adapted to an arbitrary set of given singular values. Moreover, under some mild assumptions, we prove its quadratic convergence in the root sense. Numerical experiments show that the effectiveness and practicality of the proposed method.
2021年，针对奇异值反问题，设计了基于矩阵乘法的二次收敛算法（Wei and Chen, 2021） （Ogita and Aishima, 2020）。虽然与其他二次收敛方法相比，该方法具有一些较好的特点，但并不适用于多个奇异值。本文提出了一种改进的算法，适用于给定奇异值的任意集合。此外，在一些温和的假设下，我们证明了它在根意义上的二次收敛性。数值实验表明了该方法的有效性和实用性。
{"title":"A quadratically convergent algorithm for inverse singular value problems with multiple singular values","authors":"Wei Ma, Yuqing Zhu","doi":"10.1016/j.rinam.2026.100694","DOIUrl":"10.1016/j.rinam.2026.100694","url":null,"abstract":"<div><div>In 2021, for inverse singular value problems, a quadratically convergent algorithm (Wei and Chen, 2021) based on matrix multiplication (Ogita and Aishima, 2020) was designed for inverse singular value problems. Although this method has some good features compared to other quadratic convergence methods, it is not suitable for multiple singular values. In this paper, we propose a modified algorithm adapted to an arbitrary set of given singular values. Moreover, under some mild assumptions, we prove its quadratic convergence in the root sense. Numerical experiments show that the effectiveness and practicality of the proposed method.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100694"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147395546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study introduces a hybrid numerical methodology designed to address multi-domain wave propagation problems. The temporal discretization is achieved using the Houbolt scheme, a finite-difference-based approach known for its robust stability in time-dependent simulations. Spatially, the computational domain is partitioned into subdomains via a domain decomposition strategy, with continuity and equilibrium constraints imposed along the interfaces to ensure physical fidelity. Within each subdomain, the meshless generalized finite difference method (GFDM) is employed, thereby avoiding the complexity of mesh generation. Through the integration of Taylor series expansion and moving least squares (MLS) approximation, explicit formulations of partial derivatives are constructed. Numerical experiments confirm that the proposed hybrid method provides high accuracy and stability in simulating multi-domain wave propagation phenomena.
{"title":"A hybrid numerical method for multi-domain wave propagation problems","authors":"Zihui Yan , Xiangran Zheng , Wenzhen Qu , Sheng-Dong Zhao","doi":"10.1016/j.rinam.2025.100678","DOIUrl":"10.1016/j.rinam.2025.100678","url":null,"abstract":"<div><div>This study introduces a hybrid numerical methodology designed to address multi-domain wave propagation problems. The temporal discretization is achieved using the Houbolt scheme, a finite-difference-based approach known for its robust stability in time-dependent simulations. Spatially, the computational domain is partitioned into subdomains via a domain decomposition strategy, with continuity and equilibrium constraints imposed along the interfaces to ensure physical fidelity. Within each subdomain, the meshless generalized finite difference method (GFDM) is employed, thereby avoiding the complexity of mesh generation. Through the integration of Taylor series expansion and moving least squares (MLS) approximation, explicit formulations of partial derivatives are constructed. Numerical experiments confirm that the proposed hybrid method provides high accuracy and stability in simulating multi-domain wave propagation phenomena.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100678"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-01-31DOI: 10.1016/j.rinam.2026.100685
Muhammad Asif , Fatima , Muhammad Bilal Riaz , Faisal Bilal
Telegraph interface models accurately predict signal and wave behavior in layered media with multiple boundaries, providing a reliable basis for the design and analysis of electrical, communication, and geophysical systems. This article presents a numerical method for solving the one-dimensional telegraph equation with double interface conditions. The proposed scheme combines radial basis functions for spatial discretization with finite difference approximations in time, forming a unified and flexible computational framework. This hybrid approach is capable of handling both linear and nonlinear problems and can accommodate constant as well as variable coefficients. Linear algebraic systems arising from the discretization are solved using Gaussian elimination, while nonlinear problems are treated through a quasi-Newton linearization technique. The accuracy and efficiency of the method are evaluated by computing the maximum absolute error and the root mean square error for different spatial grid sizes and time step values. Numerical results confirm that the proposed scheme is easy to implement, exhibits fast convergence, and achieves high accuracy across a range of test problems. Therefore, the method provides a reliable and efficient computational tool for solving telegraph equations with interface discontinuities.
{"title":"A hybrid meshless collocation approach for capturing solution and gradient jumps in 1D telegraph double-interface model with highly discontinuous coefficients","authors":"Muhammad Asif , Fatima , Muhammad Bilal Riaz , Faisal Bilal","doi":"10.1016/j.rinam.2026.100685","DOIUrl":"10.1016/j.rinam.2026.100685","url":null,"abstract":"<div><div>Telegraph interface models accurately predict signal and wave behavior in layered media with multiple boundaries, providing a reliable basis for the design and analysis of electrical, communication, and geophysical systems. This article presents a numerical method for solving the one-dimensional telegraph equation with double interface conditions. The proposed scheme combines radial basis functions for spatial discretization with finite difference approximations in time, forming a unified and flexible computational framework. This hybrid approach is capable of handling both linear and nonlinear problems and can accommodate constant as well as variable coefficients. Linear algebraic systems arising from the discretization are solved using Gaussian elimination, while nonlinear problems are treated through a quasi-Newton linearization technique. The accuracy and efficiency of the method are evaluated by computing the maximum absolute error and the root mean square error for different spatial grid sizes and time step values. Numerical results confirm that the proposed scheme is easy to implement, exhibits fast convergence, and achieves high accuracy across a range of test problems. Therefore, the method provides a reliable and efficient computational tool for solving telegraph equations with interface discontinuities.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100685"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147395641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-01-06DOI: 10.1016/j.rinam.2025.100680
Thomas Batard
This paper deals with the application of a geometric setting widely employed in theoretical physics, namely the fiber bundles, to color image restoration. The key idea of this approach is to model an image as a function on a principal bundle satisfying an equivariance property with respect to the action of a Lie group acting on its pixel values, and which can model the lighting changes in a scene. In this context, a natural tool for the differentiation of an image is by means of a covariant derivative. In previous works, optimal covariant derivatives have been constructed as solutions of a variational model consisting of the minimization of the norm of the covariant derivative of the image, and applied to various tasks in color image restoration through the extension of the Total Variation regularizer to vector bundles. The aim of this paper is to extend these works by constructing optimal second order covariant derivatives as solutions of the minimization of the norm of the second order covariant derivative of the image. Experiments on deblurring and super-resolution corroborate the relevance of the proposed model for color image restoration. More generally, this paper validates the use of the geometric setting of fiber bundles in imaging sciences.
{"title":"Optimal second order covariant derivatives on associated bundles — Application to color image restoration","authors":"Thomas Batard","doi":"10.1016/j.rinam.2025.100680","DOIUrl":"10.1016/j.rinam.2025.100680","url":null,"abstract":"<div><div>This paper deals with the application of a geometric setting widely employed in theoretical physics, namely the fiber bundles, to color image restoration. The key idea of this approach is to model an image as a function on a principal bundle satisfying an equivariance property with respect to the action of a Lie group acting on its pixel values, and which can model the lighting changes in a scene. In this context, a natural tool for the differentiation of an image is by means of a covariant derivative. In previous works, optimal covariant derivatives have been constructed as solutions of a variational model consisting of the minimization of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm of the covariant derivative of the image, and applied to various tasks in color image restoration through the extension of the Total Variation regularizer to vector bundles. The aim of this paper is to extend these works by constructing optimal second order covariant derivatives as solutions of the minimization of the norm of the second order covariant derivative of the image. Experiments on deblurring and super-resolution corroborate the relevance of the proposed model for color image restoration. More generally, this paper validates the use of the geometric setting of fiber bundles in imaging sciences.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100680"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-12-17DOI: 10.1016/j.rinam.2025.100674
Yalin Tang , Mingjun Li , Shujiang Tang
In this study, we develop a hybrid high-order monotonicity-preserving Weighted Essentially Non-Oscillatory (MPWENO) finite difference discretization for the compressible Euler equations. The key innovation of this scheme lies in optimizing the numerical flux through the mixed smooth indicator to reduce the numerical oscillations caused by scheme conversion, and adjusting the reference value to modify the MP limiter, thereby enabling the scheme to achieve the required numerical accuracy while maintaining monotonicity. The novelty of this work lies in systematically adjusting the numerical fluxes by using the mixed smooth indicator to distinguish between discontinuities and extrema and improving the accuracy of the reference value to change the MP limiter, which is different from other MP schemes. The proposed method improves the accuracy at the extreme points, exhibits outstanding robustness and excellent resolution, making it particularly suitable for solving complex problems in compressible Euler equations. Moreover, it is easy to implement and applicable to multi-dimensional problems, with significant practical advantages. Numerical results show that this method has high accuracy, strong robustness, and high resolution. These findings highlight the effectiveness and reliability of this method in handling complex compressible flow simulations.
{"title":"A hybrid MPWENO scheme with enhanced accuracy and robustness for the compressible Euler equations","authors":"Yalin Tang , Mingjun Li , Shujiang Tang","doi":"10.1016/j.rinam.2025.100674","DOIUrl":"10.1016/j.rinam.2025.100674","url":null,"abstract":"<div><div>In this study, we develop a hybrid high-order monotonicity-preserving Weighted Essentially Non-Oscillatory (MPWENO) finite difference discretization for the compressible Euler equations. The key innovation of this scheme lies in optimizing the numerical flux through the mixed smooth indicator to reduce the numerical oscillations caused by scheme conversion, and adjusting the reference value to modify the MP limiter, thereby enabling the scheme to achieve the required numerical accuracy while maintaining monotonicity. The novelty of this work lies in systematically adjusting the numerical fluxes by using the mixed smooth indicator to distinguish between discontinuities and extrema and improving the accuracy of the reference value to change the MP limiter, which is different from other MP schemes. The proposed method improves the accuracy at the extreme points, exhibits outstanding robustness and excellent resolution, making it particularly suitable for solving complex problems in compressible Euler equations. Moreover, it is easy to implement and applicable to multi-dimensional problems, with significant practical advantages. Numerical results show that this method has high accuracy, strong robustness, and high resolution. These findings highlight the effectiveness and reliability of this method in handling complex compressible flow simulations.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100674"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-02-26DOI: 10.1016/j.rinam.2026.100689
Qinghua Wu
This paper presents a barycentric physics-informed (BPI) computational method for solving second-kind Fredholm integral equations. Unlike conventional Multi-Layer Perceptrons (MLPs) used in Physics-Informed Neural Networks (PINNs) that introduce inherent barriers to higher precision, the BPI method employs barycentric interpolation on Chebyshev nodes as the underlying approximation structure. The method treats function values at Chebyshev nodes as trainable parameters and enforces integral constraints through collocation with Clenshaw-Curtis quadrature for integral evaluation. The approximate solution is constructed using the barycentric interpolation formula with parameters optimized to minimize the integral equation residual across the domain. The BPI method achieves 10 to 25 orders of magnitude improvement over traditional neural networks. Comparative analysis against the classical Nyström method shows that BPI achieves comparable accuracy for smooth kernels and superior performance for some singular kernel. Comprehensive numerical experiments demonstrate the method’s effectiveness across diverse problem classes.
{"title":"Machine-precision solution of Fredholm integral equations via barycentric physics-informed method","authors":"Qinghua Wu","doi":"10.1016/j.rinam.2026.100689","DOIUrl":"10.1016/j.rinam.2026.100689","url":null,"abstract":"<div><div>This paper presents a barycentric physics-informed (BPI) computational method for solving second-kind Fredholm integral equations. Unlike conventional Multi-Layer Perceptrons (MLPs) used in Physics-Informed Neural Networks (PINNs) that introduce inherent barriers to higher precision, the BPI method employs barycentric interpolation on Chebyshev nodes as the underlying approximation structure. The method treats function values at Chebyshev nodes as trainable parameters and enforces integral constraints through collocation with Clenshaw-Curtis quadrature for integral evaluation. The approximate solution is constructed using the barycentric interpolation formula with parameters optimized to minimize the integral equation residual across the domain. The BPI method achieves 10 to 25 orders of magnitude improvement over traditional neural networks. Comparative analysis against the classical Nyström method shows that BPI achieves comparable accuracy for smooth kernels and superior performance for some singular kernel. Comprehensive numerical experiments demonstrate the method’s effectiveness across diverse problem classes.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100689"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147395532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-01-06DOI: 10.1016/j.rinam.2025.100670
Robert Carlson
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial differential equations on domains which are modeled as networks of one dimensional segments joined at nodes.
{"title":"A quantum graph FFT with applications to partial differential equations on networks","authors":"Robert Carlson","doi":"10.1016/j.rinam.2025.100670","DOIUrl":"10.1016/j.rinam.2025.100670","url":null,"abstract":"<div><div>The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial differential equations on domains which are modeled as networks of one dimensional segments joined at nodes.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100670"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-02-20DOI: 10.1016/j.rinam.2026.100690
Nourelhouda Taachouche, Salim Bouzebda
Quantiles constitute a fundamental construct in probability theory and mathematical statistics, serving as an indispensable tool across a wide spectrum of applications. While the univariate concept of quantiles is both intuitively transparent and mathematically well established, its extension to the multivariate domain presents profound theoretical and methodological challenges. Among the prominent approaches to multivariate quantiles, the spatial (or geometric) framework has emerged as a particularly powerful paradigm. Its empirical counterparts not only demonstrate notable robustness but also admit an elegant Bahadur–Kiefer-type representation, thereby bridging classical theory with modern inference. In this work, we develop a comprehensive theory of conditional spatial quantiles for data residing on a general unit hypersphere and subject to measurement errors—a setting that frequently arises in contemporary statistical applications. We introduce a novel deconvolution methodology for conditional spatial quantiles and provide, for the first time, a rigorous analysis of its convergence rate and asymptotic distribution. Our unified treatment establishes broad asymptotic properties under minimal structural assumptions, thereby offering a flexible and theoretically sound foundation for quantile-based inference in high-dimensional and error-contaminated environments. The theoretical developments are further substantiated through a Monte Carlo investigation designed to elucidate the finite-sample behaviour of the proposed methodology. These simulations systematically assess empirical convergence rates, quantify the impact of spectral truncation, and evaluate the stability and efficiency of the estimator. In addition, the methodology is illustrated on a real-data example, providing an empirical validation of its applicability in realistic measurement-error settings and demonstrating the operational relevance of the theoretical results beyond the asymptotic framework.
{"title":"Multivariate spatial conditional quantiles on hyperspheres in the presence of measurement error","authors":"Nourelhouda Taachouche, Salim Bouzebda","doi":"10.1016/j.rinam.2026.100690","DOIUrl":"10.1016/j.rinam.2026.100690","url":null,"abstract":"<div><div>Quantiles constitute a fundamental construct in probability theory and mathematical statistics, serving as an indispensable tool across a wide spectrum of applications. While the univariate concept of quantiles is both intuitively transparent and mathematically well established, its extension to the multivariate domain presents profound theoretical and methodological challenges. Among the prominent approaches to multivariate quantiles, the spatial (or geometric) framework has emerged as a particularly powerful paradigm. Its empirical counterparts not only demonstrate notable robustness but also admit an elegant Bahadur–Kiefer-type representation, thereby bridging classical theory with modern inference. In this work, we develop a comprehensive theory of conditional spatial quantiles for data residing on a general unit hypersphere and subject to measurement errors—a setting that frequently arises in contemporary statistical applications. We introduce a novel deconvolution methodology for conditional spatial quantiles and provide, for the first time, a rigorous analysis of its convergence rate and asymptotic distribution. Our unified treatment establishes broad asymptotic properties under minimal structural assumptions, thereby offering a flexible and theoretically sound foundation for quantile-based inference in high-dimensional and error-contaminated environments. The theoretical developments are further substantiated through a Monte Carlo investigation designed to elucidate the finite-sample behaviour of the proposed methodology. These simulations systematically assess empirical convergence rates, quantify the impact of spectral truncation, and evaluate the stability and efficiency of the estimator. In addition, the methodology is illustrated on a real-data example, providing an empirical validation of its applicability in realistic measurement-error settings and demonstrating the operational relevance of the theoretical results beyond the asymptotic framework.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100690"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147395643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-12-06DOI: 10.1016/j.rinam.2025.100677
Jiadong Qiu , Xiang Liu , Feng Liao
In this paper, general conservative sixth- and eighth-order compact finite difference schemes are presented to solve the N-coupled nonlinear Schrödinger-Boussinesq equations numerically. The existence of the difference solution is proved by fixed-point theorem. By utilizing the discrete energy methods, the proposed difference schemes are proved to be unconditionally convergent at the order with mesh-size and time step in the discrete -norm. By using the Yoshida’s composition method, we improve the scheme (3.1)-(3.3) with a group of given time-step increments repeatedly and then obtain a temporal fourth-order difference scheme. Numerical experiments confirm the theoretical results and verify the accuracy and efficiency of our method.
{"title":"General conservative sixth- and eighth-order compact finite difference schemes for the N-coupled Schrödinger-Boussinesq equations","authors":"Jiadong Qiu , Xiang Liu , Feng Liao","doi":"10.1016/j.rinam.2025.100677","DOIUrl":"10.1016/j.rinam.2025.100677","url":null,"abstract":"<div><div>In this paper, general conservative sixth- and eighth-order compact finite difference schemes are presented to solve the N-coupled nonlinear Schrödinger-Boussinesq equations numerically. The existence of the difference solution is proved by fixed-point theorem. By utilizing the discrete energy methods, the proposed difference schemes are proved to be unconditionally convergent at the order <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>8</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> with mesh-size <span><math><mi>h</mi></math></span> and time step <span><math><mi>τ</mi></math></span> in the discrete <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span>-norm. By using the Yoshida’s composition method, we improve the scheme <span><span>(3.1)</span></span>-<span><span>(3.3)</span></span> with a group of given time-step increments repeatedly and then obtain a temporal fourth-order difference scheme. Numerical experiments confirm the theoretical results and verify the accuracy and efficiency of our method.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"29 ","pages":"Article 100677"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-09-27DOI: 10.1016/j.rinam.2025.100647
M.O. Aibinu , A. Shoukat , F.M. Mahomed
The logistic growth model is a classical framework for describing constrained growth phenomena, widely applied in areas such as population dynamics, epidemiology, and resource management. This study presents a generalized extension using Atangana–Baleanu in Caputo sense (ABC)-type fractional derivatives. Proportional time delay is also included, allowing the model to capture memory-dependent and nonlocal dynamics not addressed in classical formulations. Free parameters provide flexibility for modeling complex growth in industrial, medical, and social systems. The Hybrid Sumudu Variational (HSV) method is employed to efficiently obtain semi-analytical solutions. Results highlight the combined effects of fractional order and delay on system behavior. This approach demonstrates the novelty of integrating ABC-type derivatives, proportional delay, and HSV-based solutions for real-world applications.
{"title":"Fractional logistic growth with memory effects: A tool for industry-oriented modeling","authors":"M.O. Aibinu , A. Shoukat , F.M. Mahomed","doi":"10.1016/j.rinam.2025.100647","DOIUrl":"10.1016/j.rinam.2025.100647","url":null,"abstract":"<div><div>The logistic growth model is a classical framework for describing constrained growth phenomena, widely applied in areas such as population dynamics, epidemiology, and resource management. This study presents a generalized extension using Atangana–Baleanu in Caputo sense (ABC)-type fractional derivatives. Proportional time delay is also included, allowing the model to capture memory-dependent and nonlocal dynamics not addressed in classical formulations. Free parameters provide flexibility for modeling complex growth in industrial, medical, and social systems. The Hybrid Sumudu Variational (HSV) method is employed to efficiently obtain semi-analytical solutions. Results highlight the combined effects of fractional order and delay on system behavior. This approach demonstrates the novelty of integrating ABC-type derivatives, proportional delay, and HSV-based solutions for real-world applications.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100647"},"PeriodicalIF":1.3,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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