Iterative and Petrov-Galerkin methods for solving a system of one-dimensional nonlinear elliptic equations

Guo, Ben Yu; Miller, J. J. H.

doi:10.1090/S0025-5718-1992-1122057-9

Iterative and Petrov-Galerkin methods for solving a system of one-dimensional nonlinear elliptic equations
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by Ben Yu Guo and J. J. H. Miller PDF

Math. Comp. 58 (1992), 531-547 Request permission

Abstract:

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.

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Difference methods for partial differential equations