Pub Date : 2023-10-03DOI: 10.1080/00207160.2023.2266757
Jie He, Shuaibin Gao, Weijun Zhan, Qian Guo
AbstractIn this paper, we propose a truncated Euler-Maruyama scheme for stochastic differential equations driven by fractional Brownian motion with super-linear drift coefficient. Meanwhile, the convergence rate of the numerical method is established. Numerical example is demonstrated to verify the theoretical results.Keywords: Truncated Euler–Maruyamastochastic differential equationfractional Brownian motionconvergence rateDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThis work was supported by the National Natural Science Foundation of China (11871343).5. References
{"title":"Truncated Euler–Maruyama method for stochastic differential equations driven by fractional Brownian motion with super-linear drift coefficient","authors":"Jie He, Shuaibin Gao, Weijun Zhan, Qian Guo","doi":"10.1080/00207160.2023.2266757","DOIUrl":"https://doi.org/10.1080/00207160.2023.2266757","url":null,"abstract":"AbstractIn this paper, we propose a truncated Euler-Maruyama scheme for stochastic differential equations driven by fractional Brownian motion with super-linear drift coefficient. Meanwhile, the convergence rate of the numerical method is established. Numerical example is demonstrated to verify the theoretical results.Keywords: Truncated Euler–Maruyamastochastic differential equationfractional Brownian motionconvergence rateDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThis work was supported by the National Natural Science Foundation of China (11871343).5. References","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135739674","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}
In this article we implement a method for the computation of a nonlinear elliptic problem with nonstandard growth driven by the Laplacian operator. Our implementation is based in the decomposition–coordination method that allows us, via an iterative process, to solve in each step a linear differential equation and a nonlinear algebraic equation. Our code is implemented in MatLab in two dimensions and turns out to be extremely efficient from the computational point of view.
{"title":"Effective numerical computation of p(x)-Laplace equations in 2D","authors":"Adriana Aragón, Julián Fernández Bonder, Diana Rubio","doi":"10.1080/00207160.2023.2263103","DOIUrl":"https://doi.org/10.1080/00207160.2023.2263103","url":null,"abstract":"In this article we implement a method for the computation of a nonlinear elliptic problem with nonstandard growth driven by the Laplacian operator. Our implementation is based in the decomposition–coordination method that allows us, via an iterative process, to solve in each step a linear differential equation and a nonlinear algebraic equation. Our code is implemented in MatLab in two dimensions and turns out to be extremely efficient from the computational point of view.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135323624","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}
Pub Date : 2023-09-29DOI: 10.1080/00207160.2023.2266068
Gobinda Garai, Bankim C. Mandal
AbstractIn this paper, we propose and present a non-overlapping substructuring type iterative algorithm for the Cahn-Hilliard (CH) equation, which is a prototype for phase-field models. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of CH equation has. Here we present a formulation for the linear and non-linear Dirichlet-Neumann (DN) method applied to the CH equation and study the convergence behaviour in one and two spatial dimension in multiple subdomains. We show numerical experiments to illustrate our theoretical findings and effectiveness of the method.Keywords: Dirichlet-NeumannCahn-Hilliard equationParallel computingDomain decompositionConvergence analysisAMS subject classifications: 65M5565Y0565M15DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe authors would like to thank the CSIR India (File No:09/1059(0019)/2018-EMR-I) and DST-SERB (File No: SRG/2019/002164) for the financial assistance and IIT Bhubaneswar for research facility.
{"title":"Linear and Nonlinear Dirichlet-Neumann Method in Multiple Subdomains for the Cahn-Hilliard Equation","authors":"Gobinda Garai, Bankim C. Mandal","doi":"10.1080/00207160.2023.2266068","DOIUrl":"https://doi.org/10.1080/00207160.2023.2266068","url":null,"abstract":"AbstractIn this paper, we propose and present a non-overlapping substructuring type iterative algorithm for the Cahn-Hilliard (CH) equation, which is a prototype for phase-field models. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of CH equation has. Here we present a formulation for the linear and non-linear Dirichlet-Neumann (DN) method applied to the CH equation and study the convergence behaviour in one and two spatial dimension in multiple subdomains. We show numerical experiments to illustrate our theoretical findings and effectiveness of the method.Keywords: Dirichlet-NeumannCahn-Hilliard equationParallel computingDomain decompositionConvergence analysisAMS subject classifications: 65M5565Y0565M15DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe authors would like to thank the CSIR India (File No:09/1059(0019)/2018-EMR-I) and DST-SERB (File No: SRG/2019/002164) for the financial assistance and IIT Bhubaneswar for research facility.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135247591","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}
Pub Date : 2023-09-28DOI: 10.1080/00207160.2023.2262056
Kamel Benyettou, Djillali Bouagada, Mohammed Amine Ghezzar
AbstractThe effectiveness of this paper lies in presenting a new solution for the singular fractional two dimensional linear continuous-time systems using the conformable derivative and Sumudu transform. The proposed technique combines the new advantageous features of conformal derivative and double-delta-Kronecker, which efficiently handles singularities and Sumudu transform, and provides an efficient solution for 2D singular Fornasini-Marchesini fractional models. Applying these approaches, we then derive new explicit expressions for the fundamental matrices of the considered model. The applicability and usefulness of our proposed methods are validated and evaluated by numerical simulations in order to show the accuracy of the obtained results.Keywords: Fractional linear systemsConformable derivativeDouble Laplace transformDouble Sumudu transformFornasini-Marchesini modelsFundamental matrixSingular systemsDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThis paper presents research results of the ACSY-Team (Analysis & Control systems team) and of the doctorial training on the Operational Research from the Pure and Applied mathematics Laboratory UMAB and Decision Support funded by the General Directorate for Scientific Research and Technological Development of Algeria (DGRSDT) and supported by National Higher School of Mathematics (NHSM), University of Mostaganem Abdelhamid Ibn Badis (UMAB) and initiated by the concerted research project on Control and Systems theory (PRFU Project Code C00L03UN270120200003).
摘要本文的有效性在于利用适形导数和Sumudu变换，给出了奇异分数阶二维线性连续系统的一种新的解。该方法结合了保角导数和双delta- kronecker的新优势，有效地处理了奇异性和Sumudu变换，为二维奇异Fornasini-Marchesini分数阶模型提供了一种有效的求解方法。应用这些方法，我们为所考虑的模型的基本矩阵推导出新的显式表达式。通过数值模拟验证了所提方法的适用性和有效性，从而表明所得结果的准确性。关键词:分数阶线性系统合导双拉普拉斯变换双Sumudu变换fornasini - marchesini模型基本矩阵奇异系统免责声明作为对作者和研究人员的服务，我们提供这个版本的接受稿件(AM)。在最终出版版本记录(VoR)之前，将对该手稿进行编辑、排版和审查。在制作和印前，可能会发现可能影响内容的错误，所有适用于期刊的法律免责声明也与这些版本有关。本文介绍了acsy团队(分析与控制系统团队)的研究成果，以及由阿尔及利亚科学研究与技术发展总局(DGRSDT)资助，国家高等数学学院(NHSM)支持的纯数学与应用数学实验室(UMAB和决策支持)的运筹学博士培训的研究成果。Mostaganem Abdelhamid Ibn Badis大学(UMAB)，由控制与系统理论协同研究项目(PRFU项目代码C00L03UN270120200003)发起。
{"title":"General Solution of Two-dimensional Singular Fractional Linear Continuous-Time System Using the conformable derivative and Sumudu transform","authors":"Kamel Benyettou, Djillali Bouagada, Mohammed Amine Ghezzar","doi":"10.1080/00207160.2023.2262056","DOIUrl":"https://doi.org/10.1080/00207160.2023.2262056","url":null,"abstract":"AbstractThe effectiveness of this paper lies in presenting a new solution for the singular fractional two dimensional linear continuous-time systems using the conformable derivative and Sumudu transform. The proposed technique combines the new advantageous features of conformal derivative and double-delta-Kronecker, which efficiently handles singularities and Sumudu transform, and provides an efficient solution for 2D singular Fornasini-Marchesini fractional models. Applying these approaches, we then derive new explicit expressions for the fundamental matrices of the considered model. The applicability and usefulness of our proposed methods are validated and evaluated by numerical simulations in order to show the accuracy of the obtained results.Keywords: Fractional linear systemsConformable derivativeDouble Laplace transformDouble Sumudu transformFornasini-Marchesini modelsFundamental matrixSingular systemsDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThis paper presents research results of the ACSY-Team (Analysis & Control systems team) and of the doctorial training on the Operational Research from the Pure and Applied mathematics Laboratory UMAB and Decision Support funded by the General Directorate for Scientific Research and Technological Development of Algeria (DGRSDT) and supported by National Higher School of Mathematics (NHSM), University of Mostaganem Abdelhamid Ibn Badis (UMAB) and initiated by the concerted research project on Control and Systems theory (PRFU Project Code C00L03UN270120200003).","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343614","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}
Pub Date : 2023-09-25DOI: 10.1080/00207160.2023.2260007
Khedidja Kherchouche, Azzeddine Bellour, Pedro Lima
AbstractIn this paper, we discuss the application of an iterative collocation method based on the use of Lagrange polynomials for the numerical solution of a class of nonlinear third kind Volterra integral equations. The approximate solution is given by explicit formulas. The error analysis of the proposed numerical method is studied theoretically. Some numerical examples are given to confirm our theoretical results.Keywords: Nonlinear third kind Volterra integral equationCollocation methodIterative methodLagrange polynomialsConvergence analysis.DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe third author (P. Lima) acknowledges financial support from FCT, through projects UIDB/04621/2020, UIDP/04621/2020.
{"title":"Numerical solution of nonlinear third kind Volterra integral equations using an iterative collocation method","authors":"Khedidja Kherchouche, Azzeddine Bellour, Pedro Lima","doi":"10.1080/00207160.2023.2260007","DOIUrl":"https://doi.org/10.1080/00207160.2023.2260007","url":null,"abstract":"AbstractIn this paper, we discuss the application of an iterative collocation method based on the use of Lagrange polynomials for the numerical solution of a class of nonlinear third kind Volterra integral equations. The approximate solution is given by explicit formulas. The error analysis of the proposed numerical method is studied theoretically. Some numerical examples are given to confirm our theoretical results.Keywords: Nonlinear third kind Volterra integral equationCollocation methodIterative methodLagrange polynomialsConvergence analysis.DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe third author (P. Lima) acknowledges financial support from FCT, through projects UIDB/04621/2020, UIDP/04621/2020.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135768938","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}
Pub Date : 2023-09-21DOI: 10.1080/00207160.2023.2260011
Zhousheng Ruana, Zhenxing Chena, Min Luoa, Wen Zhang
AbstractFacing application in real world, a simultaneous identification problem of determining the initial diffusion time (or the length of diffusion time) and source term in a time fractional diffusion equation is investigated. First the simultaneous reconstruction problem is proposed by translating the Caputo fractional derivative. Then the uniqueness results for the simultaneous identification problem are proven by the technique of analytic continuation and the Laplace transformation method. Next the Lipschitz continuousness of the observation operator is derived, and an alternating direction inversion algorithm is proposed to solve the simultaneous identification problem. At last, several numerical examples are computed to show the efficiency and stability of the reconstruction algorithm.Keywords: Simultaneous identificationthe length of diffusion timeinverse source problemuniquenesstime-fractional diffusion equation2000 MR Subject Classification: 65M0665M1265M32DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThis work is supported by National Natural Science Foundation of China (12061008, 11861007, 11961002), Natural Science Foundation of Jiangxi Province of China (20202BABL 201004).
{"title":"On the simultaneous reconstruction of the initial diffusion time and source term for the time-fractional diffusion equation","authors":"Zhousheng Ruana, Zhenxing Chena, Min Luoa, Wen Zhang","doi":"10.1080/00207160.2023.2260011","DOIUrl":"https://doi.org/10.1080/00207160.2023.2260011","url":null,"abstract":"AbstractFacing application in real world, a simultaneous identification problem of determining the initial diffusion time (or the length of diffusion time) and source term in a time fractional diffusion equation is investigated. First the simultaneous reconstruction problem is proposed by translating the Caputo fractional derivative. Then the uniqueness results for the simultaneous identification problem are proven by the technique of analytic continuation and the Laplace transformation method. Next the Lipschitz continuousness of the observation operator is derived, and an alternating direction inversion algorithm is proposed to solve the simultaneous identification problem. At last, several numerical examples are computed to show the efficiency and stability of the reconstruction algorithm.Keywords: Simultaneous identificationthe length of diffusion timeinverse source problemuniquenesstime-fractional diffusion equation2000 MR Subject Classification: 65M0665M1265M32DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThis work is supported by National Natural Science Foundation of China (12061008, 11861007, 11961002), Natural Science Foundation of Jiangxi Province of China (20202BABL 201004).","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136129480","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}
Pub Date : 2023-09-06DOI: 10.1080/00207160.2023.2254412
Jinfeng Zhou, Xian-Ming Gu, Yong-Liang Zhao, Hu Li
The Black-Scholes (B-S) equation has been recently extended as a kind of tempered time-fractional B-S equations, which becomes an interesting mathematical model in option pricing. In this study, we provide a fast numerical method to approximate the solution of the tempered time-fractional B-S model. To achieve high-order accuracy in space and overcome the weak initial singularity of exact solution, we combine the compact difference operator with L1-type approximation under nonuniform time steps to yield the numerical scheme. The convergence of the proposed difference scheme is proved to be unconditionally stable. Moreover, the kernel function in the tempered Caputo fractional derivative is approximated by sum-of-exponentials, which leads to a fast unconditionally stable compact difference method that reduces the computational cost. Finally, numerical results demonstrate the effectiveness of the proposed methods.
{"title":"A fast compact difference scheme with unequal time-steps for the tempered time-fractional Black-Scholes model","authors":"Jinfeng Zhou, Xian-Ming Gu, Yong-Liang Zhao, Hu Li","doi":"10.1080/00207160.2023.2254412","DOIUrl":"https://doi.org/10.1080/00207160.2023.2254412","url":null,"abstract":"The Black-Scholes (B-S) equation has been recently extended as a kind of tempered time-fractional B-S equations, which becomes an interesting mathematical model in option pricing. In this study, we provide a fast numerical method to approximate the solution of the tempered time-fractional B-S model. To achieve high-order accuracy in space and overcome the weak initial singularity of exact solution, we combine the compact difference operator with L1-type approximation under nonuniform time steps to yield the numerical scheme. The convergence of the proposed difference scheme is proved to be unconditionally stable. Moreover, the kernel function in the tempered Caputo fractional derivative is approximated by sum-of-exponentials, which leads to a fast unconditionally stable compact difference method that reduces the computational cost. Finally, numerical results demonstrate the effectiveness of the proposed methods.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135098101","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}
Pub Date : 2023-08-16DOI: 10.1080/00207160.2023.2248303
S. Camacho Torregrosa, C. Santamaría Navarro, X. Albert Ros
{"title":"Mathematical modelling of frailty, dependency and mortality in a 70-year-old general population.","authors":"S. Camacho Torregrosa, C. Santamaría Navarro, X. Albert Ros","doi":"10.1080/00207160.2023.2248303","DOIUrl":"https://doi.org/10.1080/00207160.2023.2248303","url":null,"abstract":"","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"20 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73796739","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}
In this paper, the conforming virtual element method (VEM) is considered to solve the two-dimensional fractional cable equation involving two Riemann–Liouville fractional derivatives. We adopt the Backward Euler Method and the classical scheme for the numerical discrete scheme of the time derivative. Meanwhile, the conforming VEM, which is generated for arbitrary order of accuracy and the arbitrary polygonal meshes, is analysed for the discretization of the spatial direction. Based on the energy projection operator, the fully discrete formula is proved to be unconditionally stable, and the optimal convergence results are derived with regard to the -norm in detail. Finally, some numerical experiments are implemented to verify the theoretical results.
{"title":"The virtual element method for solving two-dimensional fractional cable equation on general polygonal meshes","authors":"Jixiao Guo, Yanping Chen, Jianwei Zhou, Yuanfei Huang","doi":"10.1080/00207160.2023.2248288","DOIUrl":"https://doi.org/10.1080/00207160.2023.2248288","url":null,"abstract":"In this paper, the conforming virtual element method (VEM) is considered to solve the two-dimensional fractional cable equation involving two Riemann–Liouville fractional derivatives. We adopt the Backward Euler Method and the classical scheme for the numerical discrete scheme of the time derivative. Meanwhile, the conforming VEM, which is generated for arbitrary order of accuracy and the arbitrary polygonal meshes, is analysed for the discretization of the spatial direction. Based on the energy projection operator, the fully discrete formula is proved to be unconditionally stable, and the optimal convergence results are derived with regard to the -norm in detail. Finally, some numerical experiments are implemented to verify the theoretical results.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"226 1","pages":"2026 - 2046"},"PeriodicalIF":1.8,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80139567","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}
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