Реферат: 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.

Библиографическая ссылка: 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

Оригинальная: 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

Идентификаторы БД:

Web of science:	WOS:000764738500006
Scopus:	2-s2.0-85126254268
РИНЦ:	48191144
OpenAlex:	W4214943734

Цитирование в БД:

БД	Цитирований
Scopus	4
Web of science	4
OpenAlex	5
РИНЦ	4

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