Monotone iterative technique for numerical solutions of fourth-order nonlinear elliptic boundary value problems

Authors:
Yuan-Ming Wang
Affiliations:
Department of Mathematics, East China Normal University, Shanghai 200062, People's Republic of China11Corresponding address. and Division of Computational Science, E-Institute of Shanghai Universi ...
Venue:
Applied Numerical Mathematics
Year:
2007

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Abstract

This paper is concerned with finite difference solutions of a class of fourth-order nonlinear elliptic boundary value problems. The nonlinear function is not necessarily monotone. A new monotone iterative technique is developed, and three basic monotone iterative processes for the finite difference system are constructed. Several theoretical comparison results among the various monotone sequences are given. A simple and easily verified condition is obtained to guarantee a geometric convergence of the iterations. Numerical results for a model problem with known analytical solution are given.