RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Matem. Mod.: Year: Volume: Issue: Page: Find

 Matem. Mod., 2019, Volume 31, Number 6, Pages 55–81 (Mi mm4080)

On the solution of second-order linear elliptic equations

A. V. Shilkov

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow

Abstract: A method for solving interior boundary value problems for second-order linear elliptic equations by introducing ray variables is described. The region is divided into cells, within which the coefficients and sources of the equations have the smoothness and continuity properties necessary for the existence of regular solutions in the cell. The finite discontinuities of the coefficients (if any) pass along the cell boundaries. The regular solution in a cell is sought in the form of a superposition of the contributions made by volume and boundary sources placed on rays arriving at a given point from the cell boundaries. Next, a finite-analytic scheme for the numerical solution of boundary value problems in a domain with discontinuous coefficients and sources is constructed by matching the regular solutions emerging from cells at the cell boundaries. The scheme does not exhibit the rigid dependence of the accuracy of approximation on the sizes and shape of the cells, which is inherent in finite-difference schemes.

Keywords: elliptic equations, boundary value problem, method of ray variables, numerical methods, finite-analytic scheme.

 Funding Agency Grant Number Russian Science Foundation 14-11-00699

DOI: https://doi.org/10.1134/S0234087919060042

Full text: PDF file (413 kB)
References: PDF file   HTML file

Revised: 19.11.2018
Accepted:10.12.2018

Citation: A. V. Shilkov, “On the solution of second-order linear elliptic equations”, Matem. Mod., 31:6 (2019), 55–81

Citation in format AMSBIB
\Bibitem{Shi19} \by A.~V.~Shilkov \paper On the solution of second-order linear elliptic equations \jour Matem. Mod. \yr 2019 \vol 31 \issue 6 \pages 55--81 \mathnet{http://mi.mathnet.ru/mm4080} \crossref{https://doi.org/10.1134/S0234087919060042} \elib{https://elibrary.ru/item.asp?id=37424213}