A Difference Scheme and Its Error Analysis for a Poisson Equation with Nonlocal Boundary Conditions
The elliptic problem with a nonlocal boundary condition is widely applied in the field of science and engineering, such as the chaotic system. Firstly, we construct one high-accuracy difference scheme for a kind of elliptic problem by tactfully introducing an equivalent relation for one nonlocal con...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/6329404 |
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| _version_ | 1832568522961584128 |
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| author | Chunsheng Feng Cunyun Nie Haiyuan Yu Liping Zhou |
| author_facet | Chunsheng Feng Cunyun Nie Haiyuan Yu Liping Zhou |
| author_sort | Chunsheng Feng |
| collection | DOAJ |
| description | The elliptic problem with a nonlocal boundary condition is widely applied in the field of science and engineering, such as the chaotic system. Firstly, we construct one high-accuracy difference scheme for a kind of elliptic problem by tactfully introducing an equivalent relation for one nonlocal condition. Then, we obtain the local truncation error equation by the Taylor formula and, initially, prove that the new scheme can reach the asymptotic optimal error estimate Oh2ln h in the maximum norm through ingeniously transforming a two-dimensional problem to a one-dimensional one through bringing in the discrete Fourier transformation. Numerical experiments demonstrate the correctness of theoretical results. |
| format | Article |
| id | doaj-art-bd32fcdb2a764364a93bba62c7cd8888 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-bd32fcdb2a764364a93bba62c7cd88882025-02-03T00:58:57ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/63294046329404A Difference Scheme and Its Error Analysis for a Poisson Equation with Nonlocal Boundary ConditionsChunsheng Feng0Cunyun Nie1Haiyuan Yu2Liping Zhou3Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, ChinaSchool of Mathematics and Physics, Hunan Institution of Engineering, Xiangtan 411105, ChinaHunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, ChinaCollege of Science, Hunan University of Science and Engineering, Yongzhou 425199, ChinaThe elliptic problem with a nonlocal boundary condition is widely applied in the field of science and engineering, such as the chaotic system. Firstly, we construct one high-accuracy difference scheme for a kind of elliptic problem by tactfully introducing an equivalent relation for one nonlocal condition. Then, we obtain the local truncation error equation by the Taylor formula and, initially, prove that the new scheme can reach the asymptotic optimal error estimate Oh2ln h in the maximum norm through ingeniously transforming a two-dimensional problem to a one-dimensional one through bringing in the discrete Fourier transformation. Numerical experiments demonstrate the correctness of theoretical results.http://dx.doi.org/10.1155/2020/6329404 |
| spellingShingle | Chunsheng Feng Cunyun Nie Haiyuan Yu Liping Zhou A Difference Scheme and Its Error Analysis for a Poisson Equation with Nonlocal Boundary Conditions Complexity |
| title | A Difference Scheme and Its Error Analysis for a Poisson Equation with Nonlocal Boundary Conditions |
| title_full | A Difference Scheme and Its Error Analysis for a Poisson Equation with Nonlocal Boundary Conditions |
| title_fullStr | A Difference Scheme and Its Error Analysis for a Poisson Equation with Nonlocal Boundary Conditions |
| title_full_unstemmed | A Difference Scheme and Its Error Analysis for a Poisson Equation with Nonlocal Boundary Conditions |
| title_short | A Difference Scheme and Its Error Analysis for a Poisson Equation with Nonlocal Boundary Conditions |
| title_sort | difference scheme and its error analysis for a poisson equation with nonlocal boundary conditions |
| url | http://dx.doi.org/10.1155/2020/6329404 |
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