Finite difference method for boundary value problem for nonlinear elliptic equation with nonlocal conditions

Boundary Value Problems

Kristina Jakubėlienė¹  Mifodijus Sapagovas²  Olga Štikonienė³  Regimantas Čiupaila⁴ 

[1] 0000 0001 1091 4533, grid.6901.e, Department of Applied Mathematics, Kaunas University of Technology, Kaunas, Lithuania;0000 0001 2243 2806, grid.6441.7, Faculty of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania;0000 0001 2243 2806, grid.6441.7, Institute of Applied Mathematics, Vilnius University, Vilnius, Lithuania;0000 0004 1937 1776, grid.9424.b, Vilnius Gediminas Technical University, Vilnius, Lithuania;

关键词: Elliptic equation;    Integral boundary conditions;    Convergence of finite-difference method;    Eigenvalue problem;    M-matrices;    65M06;    65M12;    65N25;   

DOI  :  10.1186/s13661-019-1202-4

来源: publisher

【 摘 要 】

In the paper the convergence of a finite difference scheme for two-dimensional nonlinear elliptic equation in the rectangular domain with the integral boundary condition is considered. The majorant is constructed for the error of the solution of the system of difference equations, and the estimation of this error is obtained. With this aim, the idea of application of the M-matrices for the theoretical investigation of the system of difference equations was developed. Main results for the convergence of the difference schemes are obtained considering the structure of the spectrum and properties of the M-matrices for a wider class of boundary value problems for nonlinear equations with nonlocal conditions. The main advantage of the suggested method is that the error of approximate solution is estimated in the maximum norm.

【 授权许可】

CC BY