Numerical method for nonlinear elliptic singularly perturbed problem. (English) Zbl 0842.65075
Some singularly perturbed nonlinear elliptic boundary value problems are transformed into integral equations. These equations are solved by a three-point finite difference scheme. The first-order uniform accuracy of this scheme is proved. A numerical example concerning a linear elliptic boundary value problem is also solved.
Reviewer: C.I.Gheorghiu (Cluj-Napoca)
MSC:
65N38 | Boundary element methods for boundary value problems involving PDEs |
35B25 | Singular perturbations in context of PDEs |
65N15 | Error bounds for boundary value problems involving PDEs |
35J65 | Nonlinear boundary value problems for linear elliptic equations |