Computational Methods in Applied Mathematics最新文献

{"title":"Variational Approximation for a Non-Isothermal Coupled Phase-Field System: Structure-Preservation & Nonlinear Stability","authors":"Aaron Brunk, Oliver Habrich, Timileyin David Oyedeji, Yangyiwei Yang, Bai-Xiang Xu","doi":"10.1515/cmam-2023-0274","DOIUrl":"https://doi.org/10.1515/cmam-2023-0274","url":null,"abstract":"A Cahn–Hilliard–Allen–Cahn phase-field model coupled with a heat transfer equation, particularly with full non-diagonal mobility matrices, is studied. After reformulating the problem with respect to the inverse of temperature, we proposed and analysed a structure-preserving approximation for the semi-discretisation in space and then a fully discrete approximation using conforming finite elements and time-stepping methods. We prove structure-preserving property and discrete stability using relative entropy methods for the semi-discrete and fully discrete case. The theoretical results are illustrated by numerical experiments.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"48 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Space-Time Finite Element Method for the Eddy Current Approximation of Rotating Electric Machines","authors":"Peter Gangl, Mario Gobrial, Olaf Steinbach","doi":"10.1515/cmam-2024-0033","DOIUrl":"https://doi.org/10.1515/cmam-2024-0033","url":null,"abstract":"In this paper we formulate and analyze a space-time finite element method for the numerical simulation of rotating electric machines where the finite element mesh is fixed in a space-time domain. Based on the Babuška–Nečas theory we prove unique solvability both for the continuous variational formulation and for a standard Galerkin finite element discretization in the space-time domain. This approach allows for an adaptive resolution of the solution both in space and time, but it requires the solution of the overall system of algebraic equations. While the use of parallel solution algorithms seems to be mandatory, this also allows for a parallelization simultaneously in space and time. This approach is used for the eddy current approximation of the Maxwell equations which results in an elliptic-parabolic interface problem. Numerical results for linear and nonlinear constitutive material relations confirm the applicability and accuracy of the proposed approach.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"2 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Inverse Matrix Eigenvalue Problem for Constructing a Vibrating Rod","authors":"Hanif Mirzaei, Vahid Abbasnavaz, Kazem Ghanbari","doi":"10.1515/cmam-2024-0001","DOIUrl":"https://doi.org/10.1515/cmam-2024-0001","url":null,"abstract":"The free longitudinal vibrations of a rod are described by a differential equation of the form <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msup> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>P</m:mi> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mi>y</m:mi> <m:mo>′</m:mo> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>′</m:mo> </m:msup> <m:mo>+</m:mo> <m:mi>λ</m:mi> <m:mi>P</m:mi> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mi>y</m:mi> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2024-0001_eq_0062.png\"/> <jats:tex-math>{(P(x)yprime)^{prime}+lambda P(x)y(x)=0}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>P</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2024-0001_eq_0397.png\"/> <jats:tex-math>{P(x)}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the cross section area at point <jats:italic>x</jats:italic> and λ is an eigenvalue parameter. In this paper, first we discretize this differential equation by using the finite difference method to obtain a matrix eigenvalue problem of the form <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mi>𝐀</m:mi> <m:mo>⁢</m:mo> <m:mi>Y</m:mi> </m:mrow> <m:mo>=</m:mo> <m:mrow> <m:mi mathvariant=\"normal\">Λ</m:mi> <m:mo>⁢</m:mo> <m:mi>𝐁</m:mi> <m:mo>⁢</m:mo> <m:mi>Y</m:mi> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2024-0001_eq_0437.png\"/> <jats:tex-math>{mathbf{A}Y=Lambdamathbf{B}Y}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>𝐀</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2024-0001_eq_0439.png\"/> <jats:tex-math>{mathbf{A}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>𝐁</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2024-0001_eq_0440.png\"/> <jats:tex-math>{mathbf{B}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> are Jacobi and diagonal matrices dependent to cross section <jats:inline-formula> <jats:alter","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"69 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Error Estimates of a discontinuous Galerkin Method of the Boussinesq System of Equations","authors":"Saumya Bajpai, Debendra Kumar Swain","doi":"10.1515/cmam-2023-0202","DOIUrl":"https://doi.org/10.1515/cmam-2023-0202","url":null,"abstract":"In this paper, we propose and analyze a discontinuous Galerkin finite element method for solving the transient Boussinesq incompressible heat conducting fluid flow equations. This method utilizes an upwind approach to handle the nonlinear convective terms effectively. We discuss new a priori bounds for the semidiscrete discontinuous Galerkin approximations. Furthermore, we establish optimal a priori error estimates for the semidiscrete discontinuous Galerkin velocity approximation in <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi mathvariant=\"bold\">L</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2023-0202_ineq_0001.png\"/> <jats:tex-math>mathbf{L}^{2}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and energy norms, the temperature approximation in <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>L</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2023-0202_ineq_0002.png\"/> <jats:tex-math>L^{2}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and energy norms and pressure approximation in <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>L</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2023-0202_ineq_0002.png\"/> <jats:tex-math>L^{2}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-norm for <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>t</m:mi> <m:mo>&gt;</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2023-0202_ineq_0004.png\"/> <jats:tex-math>t&gt;0</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Additionally, under the smallness assumption on the data, we prove uniform in time error estimates. We also consider a backward Euler scheme for full discretization and derive fully discrete error estimates. Finally, we provide numerical examples to support the theoretical conclusions.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"24 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141587700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 2)","authors":"Michael Feischl, Dirk Praetorius, Michele Ruggeri","doi":"10.1515/cmam-2024-0090","DOIUrl":"https://doi.org/10.1515/cmam-2024-0090","url":null,"abstract":"This paper introduces the contents of the second of two special issues associated with the 9th International Conference on Computational Methods in Applied Mathematics, which took place from August 29 to September 2, 2022 in Vienna. It comments on the topics and highlights of all twelve papers of the special issue.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"213 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Space-Time FEM for the Vectorial Wave Equation under Consideration of Ohm’s Law","authors":"Julia I. M. Hauser","doi":"10.1515/cmam-2023-0079","DOIUrl":"https://doi.org/10.1515/cmam-2023-0079","url":null,"abstract":"The ability to deal with complex geometries and to go to higher orders is the main advantage of space-time finite element methods. Therefore, we want to develop a solid background from which we can construct appropriate space-time methods. In this paper, we will treat time as another space direction, which is the main idea of space-time methods. First, we will briefly discuss how exactly the vectorial wave equation is derived from Maxwell’s equations in a space-time structure, taking into account Ohm’s law. Then we will derive a space-time variational formulation for the vectorial wave equation using different trial and test spaces. This paper has two main goals. First, we prove unique solvability for the resulting Galerkin–Petrov variational formulation. Second, we analyze the discrete equivalent of the equation in a tensor product and show conditional stability, i.e., under a CFL condition. Understanding the vectorial wave equation and the corresponding space-time finite element methods is crucial for improving the existing theory of Maxwell’s equations and paves the way to computations of more complicated electromagnetic problems.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"214 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Anisotropic Adaptive Finite Elements for a p-Laplacian Problem","authors":"Paride Passelli, Marco Picasso","doi":"10.1515/cmam-2022-0205","DOIUrl":"https://doi.org/10.1515/cmam-2022-0205","url":null,"abstract":"The <jats:italic>p</jats:italic>-Laplacian problem <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mo>-</m:mo> <m:mrow> <m:mo>∇</m:mo> <m:mo>⋅</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi>μ</m:mi> <m:mo>+</m:mo> <m:msup> <m:mrow> <m:mo stretchy=\"false\">|</m:mo> <m:mrow> <m:mo>∇</m:mo> <m:mo>⁡</m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo stretchy=\"false\">|</m:mo> </m:mrow> <m:mrow> <m:mi>p</m:mi> <m:mo>-</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>⁢</m:mo> <m:mrow> <m:mo>∇</m:mo> <m:mo>⁡</m:mo> <m:mi>u</m:mi> </m:mrow> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:mrow> <m:mo>=</m:mo> <m:mi>f</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2022-0205_eq_0199.png\"/> <jats:tex-math>{-nablacdot((mu+|nabla u|^{p-2})nabla u)=f}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is considered, where μ is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher order terms, to the error in a quasi-norm. The involved constants being independent of μ, the solution, the mesh size and aspect ratio. An adaptive algorithm is proposed and numerical results are presented when <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>p</m:mi> <m:mo>=</m:mo> <m:mn>3</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2022-0205_eq_0387.png\"/> <jats:tex-math>{p=3}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. From this model problem, we propose a simplified error estimator and use it in the framework of an industrial application, namely a nonlinear Navier–Stokes problem arising from aluminium electrolysis.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"2016 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On an Optimal AFEM for Elastoplasticity","authors":"Miriam Schönauer, Andreas Schröder","doi":"10.1515/cmam-2024-0052","DOIUrl":"https://doi.org/10.1515/cmam-2024-0052","url":null,"abstract":"In this paper, optimal convergence for an adaptive finite element algorithm for elastoplasticity is considered. To this end, the proposed adaptive algorithm is established within the abstract framework of the axioms of adaptivity [C. Carstensen, M. Feischl, M. Page and D. Praetorius, Axioms of adaptivity, Comput. Math. Appl. 67 2014, 6, 1195–1253], which provides a specific proceeding to prove the optimal convergence of the scheme. The proceeding is based on verifying four axioms, which ensure the optimal convergence. The verification is done by using results from [C. Carstensen, A. Schröder and S. Wiedemann, An optimal adaptive finite element method for elastoplasticity, Numer. Math. 132 2016, 1, 131–154], which presents an alternative approach to optimality without explicitly relying on the axioms","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"10 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Novel Fully Decoupled Scheme for the MHD System with Variable Density","authors":"Zhaowei Wang, Danxia Wang, Hongen Jia","doi":"10.1515/cmam-2024-0004","DOIUrl":"https://doi.org/10.1515/cmam-2024-0004","url":null,"abstract":"In this paper, we first establish a novel first-order, fully decoupled, unconditionally stable time discretization scheme for the MHD system with variable density. This scheme successfully decouples all the coupling terms by combining the gauge-Uzawa method and the scalar auxiliary variable (SAV) method. And we prove its unconditional energy stability. Then we give the first-order finite element scheme and its implementation. Furthermore, we perform a rigorous error analysis of the proposed numerical scheme. Finally, we perform some numerical experiments to demonstrate the effectiveness of the decoupling scheme.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"156 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quadratic Discontinuous Galerkin Finite Element Methods for the Unilateral Contact Problem","authors":"Kamana Porwal, Tanvi Wadhawan","doi":"10.1515/cmam-2023-0015","DOIUrl":"https://doi.org/10.1515/cmam-2023-0015","url":null,"abstract":"In this article, we employ discontinuous Galerkin methods for the finite element approximation of the frictionless unilateral contact problem using quadratic finite elements over simplicial triangulation. We first develop a posteriori error estimates in the energy norm wherein, the reliability and efficiency of the proposed a posteriori error estimator is addressed. The suitable construction of the discrete Lagrange multiplier <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>𝝀</m:mi> <m:mi>𝒉</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2023-0015_eq_0416.png\" /> <jats:tex-math>{boldsymbol{lambda_{h}}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and some intermediate operators play a key role in developing a posteriori error analysis. Further, we establish an optimal a priori error estimates under the appropriate regularity assumption on the exact solution <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>𝒖</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2023-0015_eq_0479.png\" /> <jats:tex-math>{boldsymbol{u}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Numerical results presented on uniform and adaptive meshes illustrate and confirm the theoretical findings.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"34 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}