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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Bibliographic Details
Published inComplexity (New York, N.Y.) Vol. 2020; no. 2020; pp. 1 - 7
Main Authors Zhou, Liping, Yu, Haiyuan, Nie, Cunyun, Feng, Chunsheng
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
John Wiley & Sons, Inc
Hindawi Limited
Hindawi-Wiley
Subjects
Boundary conditions
Boundary value problems
Chaos theory
Error analysis
Experiments
Finite volume method
Fourier transforms
Numerical analysis
Poisson equation
Truncation errors
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Summary: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.
ISSN:1076-2787
1099-0526
DOI:10.1155/2020/6329404