Applied Numerical Mathematics最新文献

{"title":"Numerical scheme for the solution of the “bad” Boussinesq equation","authors":"Christophe Charlier ,&nbsp;Daniel Eriksson ,&nbsp;Jonatan Lenells","doi":"10.1016/j.apnum.2025.06.011","DOIUrl":"10.1016/j.apnum.2025.06.011","url":null,"abstract":"<div><div>We present a numerical scheme for the solution of the initial-value problem for the “bad” Boussinesq equation. The accuracy of the scheme is tested by comparison with exact soliton solutions as well as with recently obtained asymptotic formulas for the solution.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 216-233"},"PeriodicalIF":2.2,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144489529","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}

{"title":"Numerical simulation of a dynamic human capital model with demographic delays via the local discrete Galerkin method","authors":"Yadollah Ordokhani ,&nbsp;Alireza Hosseinian ,&nbsp;Pouria Assari","doi":"10.1016/j.apnum.2025.06.007","DOIUrl":"10.1016/j.apnum.2025.06.007","url":null,"abstract":"<div><div>A strong and dynamic economy depends on various factors, with human capital playing a crucial role in fostering resilience and adaptability in an ever-changing world. Human capital, which depends on the past behavior of the system, requires strategic investments in education, health, and skill development. This study presents a numerical approach for solving the human capital model with age-structured delays, formulated as integro-differential equations with double delays and difference kernels. The proposed method employs a local meshless discrete Galerkin approach based on the moving least squares (MLS) technique, which can work with irregular or non-uniform data. The localized nature of the MLS scheme enhances computational efficiency by focusing on small neighborhoods. Moreover, the stabilized MLS framework, achieved by using shifted and scaled polynomial basis functions, enhances numerical stability and reduces sensitivity to the distribution of nodes, thereby transferring these advantageous properties to the method. The simplicity of the proposed algorithm makes it easy to implement on standard personal computers and extend to a wider class of delay integro-differential equations. To assess its reliability, we analyzed its error and determined the convergence order of the presented method. We have applied it to solve several numerical examples, and the obtained results confirm the method's accuracy, stability, and alignment with theoretical findings.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 234-254"},"PeriodicalIF":2.2,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144489530","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}

{"title":"Note on an inertial projection-based approach for solving extended general quasi-variational inequalities and its convergence analysis","authors":"Saudia Jabeen ,&nbsp;Siegfried Macías ,&nbsp;Saleem Ullah ,&nbsp;Muhammad Aslam Noor ,&nbsp;Jorge E. Macías-Díaz","doi":"10.1016/j.apnum.2025.06.012","DOIUrl":"10.1016/j.apnum.2025.06.012","url":null,"abstract":"<div><div>In this work, an inertial projection-based method is proposed to find approximate solutions to a new class of quasi-variational inequalities. The approach utilizes projection techniques to develop an iterative scheme, and its convergence properties are rigorously examined under appropriate conditions. Various specific cases are derived from the general framework, highlighting the adaptability of the proposed method. The comparative performance of this approach with existing techniques remains an open area for exploration. It is expected that the theoretical framework and techniques proposed in this study will stimulate further research in this domain.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 190-198"},"PeriodicalIF":2.2,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338385","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}

{"title":"Analysis of Tseng algorithm with inertial extrapolation step for stochastic variational inequality problem","authors":"Olawale K. Oyewole ,&nbsp;Seithuti P. Moshokoa ,&nbsp;Sani Salisu ,&nbsp;Yekini Shehu","doi":"10.1016/j.apnum.2025.06.008","DOIUrl":"10.1016/j.apnum.2025.06.008","url":null,"abstract":"<div><div>In this paper, we design an inertial version of the Tseng extragradient algorithm (also called the Forward-Backward-Forward Algorithm) with self-adaptive step sizes to solve the stochastic variational inequality problem. We prove that the sequence of iterates generated by our proposed algorithm converges to a solution of the stochastic variational inequality problem under mild conditions. Furthermore, we obtain some convergence rates and numerical simulations of our proposed algorithm with comparisons with related algorithms to show the superiority of our algorithm.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 199-215"},"PeriodicalIF":2.2,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144489745","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}

{"title":"An efficient multi projection methods for systems of Fredholm integral equations with mixed weakly singular kernels: A superconvergence approach","authors":"Krishna Murari Malav ,&nbsp;Kapil Kant ,&nbsp;Joydip Dhar ,&nbsp;Samiran Chakraborty","doi":"10.1016/j.apnum.2025.06.006","DOIUrl":"10.1016/j.apnum.2025.06.006","url":null,"abstract":"<div><div>In this article, we develop the multi-Galerkin and iterated multi-Galerkin methods to solve systems of second-kind linear Fredholm integral equations (FIEs) with smooth and mixed weakly singular kernels. First, we develop the mathematical formulation of the multi-Galerkin and iterated multi-Galerkin methods using piecewise polynomial approximations to solve such systems and obtain superconvergence results. These methods transform the linear system of FIEs into corresponding matrix equations. We derive error estimates and obtain the convergence analysis. We prove that the convergence rates for the multi-Galerkin method are <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>3</mn><mi>r</mi></mrow></msup><mo>)</mo></math></span> for smooth kernels and <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>r</mi><mo>−</mo><mi>α</mi></mrow></msup><mi>log</mi><mo>⁡</mo><mi>h</mi><mo>)</mo></math></span> for mixed weakly singular kernels, where <em>r</em> denote the degree of the piecewise polynomials, <em>h</em> is the norm of partitions and <span><math><mi>α</mi><mo>=</mo><munder><mi>max</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></munder><mo>⁡</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math></span>. Moreover, we establish that the iterated multi-Galerkin method achieves improved convergence rates of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>4</mn><mi>r</mi></mrow></msup><mo>)</mo></math></span> for smooth kernels and <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>r</mi><mo>+</mo><mn>2</mn><mo>(</mo><mn>1</mn><mo>−</mo><mi>α</mi><mo>)</mo></mrow></msup><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>h</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> for mixed weakly singular kernels. Hence, the results show that the iterated multi-Galerkin method improves the multi-Galerkin method. Finally, the theoretical results are validated through the numerical examples.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 172-189"},"PeriodicalIF":2.2,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322646","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}

{"title":"Localization of tumor through a non-conventional numerical shape optimization technique","authors":"Julius Fergy Tiongson Rabago","doi":"10.1016/j.apnum.2025.06.005","DOIUrl":"10.1016/j.apnum.2025.06.005","url":null,"abstract":"<div><div>This paper presents a method for estimating the shape and location of an embedded tumor using shape optimization techniques, specifically through the coupled complex boundary method. The inverse problem—characterized by a measured temperature profile and corresponding heat flux (e.g., from infrared thermography)—is reformulated as a complex boundary value problem with a complex Robin boundary condition, thereby simplifying its over-specified nature. The geometry of the tumor is identified by optimizing an objective functional that depends on the imaginary part of the solution throughout the domain. The shape derivative of the functional is derived through shape sensitivity analysis. An iterative algorithm is developed to numerically recover the tumor shape, based on the Riesz representative of the gradient and implemented using the finite element method. In addition, the mesh sensitivity of the finite element solution to the state problem is analyzed, and bounds are established for its variation with respect to mesh deformation and its gradient. Numerical examples are presented to validate the theoretical results and to demonstrate the accuracy and effectiveness of the proposed method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 135-171"},"PeriodicalIF":2.2,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307834","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}

{"title":"A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations","authors":"Yali Gao ,&nbsp;Daozhi Han ,&nbsp;Sayantan Sarkar","doi":"10.1016/j.apnum.2025.06.004","DOIUrl":"10.1016/j.apnum.2025.06.004","url":null,"abstract":"<div><div>A high order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> finite element with mass lumping on rectangular grids, the second-order convex splitting method and the pressure correction method. The unique solvability, unconditional stability, and bound-preserving properties are rigorously established. The key for bound-preservation is the discrete <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> estimate of the singular potential. Ample numerical experiments are performed to validate the desired properties of the proposed numerical scheme.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 96-111"},"PeriodicalIF":2.2,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263514","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}

{"title":"Analysis of a divergence-free element-free Galerkin method for the Navier-Stokes equations","authors":"Xiaolin Li ,&nbsp;Haiyun Dong","doi":"10.1016/j.apnum.2025.06.002","DOIUrl":"10.1016/j.apnum.2025.06.002","url":null,"abstract":"<div><div>In this paper, an efficient divergence-free element-free Galerkin (DFEFG) method is proposed for the numerical analysis of the incompressible Navier-Stokes equations. In this method, a divergence-free moving least squares (DFMLS) approximation is used to obtain the meshless approximation of the divergence-free velocity field. The properties, stability and error of the DFMLS approximation are analyzed firstly, and then the stability and error estimation of the DFEFG method are derived theoretically. Finally, numerical results demonstrate the efficiency of the proposed methods and verify the theoretical analysis.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 73-95"},"PeriodicalIF":2.2,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263513","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}

{"title":"Generalized Clenshaw-Curtis quadrature method for systems of linear ODEs with constant coefficients","authors":"Fu-Rong Lin,&nbsp;Xi Yang,&nbsp;Gui-Rong Zhang","doi":"10.1016/j.apnum.2025.06.003","DOIUrl":"10.1016/j.apnum.2025.06.003","url":null,"abstract":"<div><div>In this paper, we consider high precision numerical methods for the initial problem of systems of linear ordinary differential equations (ODEs) with constant coefficients. It is well-known that the analytic solution of such a system of linear ODEs involves a matrix exponential function and an integral whose integrand is the product of a matrix exponential and a vector-valued function. We mainly consider numerical quadrature methods for the integral term in the analytic solution and propose a generalized Clenshaw-Curtis (GCC) quadrature method. The proposed method is then applied to the initial-boundary value problem for a heat conduction equation and a Riesz space fractional diffusion equation, respectively. Numerical results are presented to demonstrate the effectiveness of the proposed method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 112-125"},"PeriodicalIF":2.2,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144272008","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}

{"title":"On steepest coordinate descent method for computing extreme eigenpairs of symmetric matrices","authors":"Zhong-Zhi Bai","doi":"10.1016/j.apnum.2025.06.001","DOIUrl":"10.1016/j.apnum.2025.06.001","url":null,"abstract":"<div><div>For solving real and symmetric eigenvalue problems of huge sizes, we propose a steepest coordinate descent method, establish its convergence theory under reasonable conditions, and show its computational effectiveness by numerical experiments.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 126-134"},"PeriodicalIF":2.2,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144298735","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}