| Title |
Finite difference method for boundary value problem for nonlinear elliptic equation with nonlocal conditions / |
| Authors |
Sapagovas, Mifodijus ; Štikonienė, Olga ; Jakubėlienė, Kristina ; Čiupaila, Regimantas |
| DOI |
10.1186/s13661-019-1202-4 |
| Full Text |
|
| Is Part of |
Boundary value problems.. London : Springer. 2019, vol. 2019, iss. 1, art. no. 94, p. 39-62.. ISSN 1687-2762. eISSN 1687-2770 |
| Keywords [eng] |
convergence of finite-difference method ; eigenvalue problem ; elliptic equation ; integral boundary conditions ; M-matrices |
| Abstract [eng] |
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. |
| Published |
London : Springer |
| Type |
Journal article |
| Language |
English |
| Publication date |
2019 |
| CC license |
|
