Analysis of Two-Level Mesh Method for Partial Integro-Differential Equation
In this paper, we present two-level mesh scheme to solve partial integro-differential equation. The proposed method is based on a finite difference method. For the first step, we use finite difference method in time and global radial basis function (RBF) finite difference (FD) in space. For the seco...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/4557844 |
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| _version_ | 1832558421306507264 |
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| author | Quan Tang Ziyang Luo Xindong Zhang Juan Liu |
| author_facet | Quan Tang Ziyang Luo Xindong Zhang Juan Liu |
| author_sort | Quan Tang |
| collection | DOAJ |
| description | In this paper, we present two-level mesh scheme to solve partial integro-differential equation. The proposed method is based on a finite difference method. For the first step, we use finite difference method in time and global radial basis function (RBF) finite difference (FD) in space. For the second step, we use the finite difference method to solve the proposed problem. This two-level mesh scheme is obtained by combining the radial basis function with finite difference. We prove the stability and convergence of scheme and show that the convergence order is Oτ2+h2, where τ and h are the time step size and space step size, respectively. The results of numerical examples are compared with analytical solutions to show the efficiency of proposed scheme. The numerical results are in good agreement with theoretical ones. |
| format | Article |
| id | doaj-art-ecb943f4a37d42cf8a67fd58b695a6e0 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-ecb943f4a37d42cf8a67fd58b695a6e02025-02-03T01:32:26ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/4557844Analysis of Two-Level Mesh Method for Partial Integro-Differential EquationQuan Tang0Ziyang Luo1Xindong Zhang2Juan Liu3School of Mathematical SciencesSchool of Mathematical SciencesSchool of Mathematical SciencesCollege of Big Data StatisticsIn this paper, we present two-level mesh scheme to solve partial integro-differential equation. The proposed method is based on a finite difference method. For the first step, we use finite difference method in time and global radial basis function (RBF) finite difference (FD) in space. For the second step, we use the finite difference method to solve the proposed problem. This two-level mesh scheme is obtained by combining the radial basis function with finite difference. We prove the stability and convergence of scheme and show that the convergence order is Oτ2+h2, where τ and h are the time step size and space step size, respectively. The results of numerical examples are compared with analytical solutions to show the efficiency of proposed scheme. The numerical results are in good agreement with theoretical ones.http://dx.doi.org/10.1155/2022/4557844 |
| spellingShingle | Quan Tang Ziyang Luo Xindong Zhang Juan Liu Analysis of Two-Level Mesh Method for Partial Integro-Differential Equation Journal of Function Spaces |
| title | Analysis of Two-Level Mesh Method for Partial Integro-Differential Equation |
| title_full | Analysis of Two-Level Mesh Method for Partial Integro-Differential Equation |
| title_fullStr | Analysis of Two-Level Mesh Method for Partial Integro-Differential Equation |
| title_full_unstemmed | Analysis of Two-Level Mesh Method for Partial Integro-Differential Equation |
| title_short | Analysis of Two-Level Mesh Method for Partial Integro-Differential Equation |
| title_sort | analysis of two level mesh method for partial integro differential equation |
| url | http://dx.doi.org/10.1155/2022/4557844 |
| work_keys_str_mv | AT quantang analysisoftwolevelmeshmethodforpartialintegrodifferentialequation AT ziyangluo analysisoftwolevelmeshmethodforpartialintegrodifferentialequation AT xindongzhang analysisoftwolevelmeshmethodforpartialintegrodifferentialequation AT juanliu analysisoftwolevelmeshmethodforpartialintegrodifferentialequation |