On an Approach to the Numerical Solution of Dirichlet Problems of Arbitrary Dimensions Full article
| Journal |
Numerical Analysis and Applications
ISSN: 1995-4239 |
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| Output data | Year: 2022, Volume: 15, Number: 1, Pages: 63-78 Pages count : 16 DOI: 10.1134/S1995423922010062 | ||||
| Tags | collocation method; decrease in computational costs; Dirichlet boundary value problem; pseudospectral method; relaxation method | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 20-71-00071 |
Abstract:
Abstract: A method of the numerical solution of Dirichlet boundary value problems for nonlinear partial differential equations of the elliptic type and of arbitrary dimensions is proposed. It takes little memory and computer time for problems with smooth solutions. The method is based on modified interpolation polynomials with Chebyshev nodes to approximate the sought-for function and on a new approach to constructing and solving the linear algebraic problems corresponding to the initial differential equations. The spectra and condition numbers of the matrices formed by the algorithm are analyzed by using interval methods. Theorems on approximation and stability of the algorithm are proved in the linear case. It is shown that the algorithm provides a considerable decrease in computational costs as compared to the classical collocation and finite difference methods.
Cite:
Semisalov B.V.
On an Approach to the Numerical Solution of Dirichlet Problems of Arbitrary Dimensions
Numerical Analysis and Applications. 2022. V.15. N1. P.63-78. DOI: 10.1134/S1995423922010062 WOS Scopus РИНЦ OpenAlex
On an Approach to the Numerical Solution of Dirichlet Problems of Arbitrary Dimensions
Numerical Analysis and Applications. 2022. V.15. N1. P.63-78. DOI: 10.1134/S1995423922010062 WOS Scopus РИНЦ OpenAlex
Original:
Семисалов Б.В.
Об одном подходе к численному решению задач Дирихле произвольной размерности
Сибирский журнал вычислительной математики. 2022. Т.25. №1. С.77-96. DOI: 10.15372/SJNM20220106 РИНЦ OpenAlex
Об одном подходе к численному решению задач Дирихле произвольной размерности
Сибирский журнал вычислительной математики. 2022. Т.25. №1. С.77-96. DOI: 10.15372/SJNM20220106 РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000764738500006 |
| Scopus: | 2-s2.0-85126254268 |
| Elibrary: | 48191144 |
| OpenAlex: | W4214943734 |