Iterative and Petrov-Galerkin methods for solving a system of one- dimensional nonlinear elliptic equations. (English) Zbl 0812.65077
Summary: Two sequences of supersolutions and subsolutions are constructed. Their limits are the solutions of a system of one-dimensional nonlinear elliptic equations. A Petrov-Galerkin scheme is proposed. The existence of solutions of the resulting discrete system is proved by an iteration which also provides a numerical method.
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
