Error and stability of monotone method for numerical solutions of fourth-order semilinear elliptic boundary value problems

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

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Abstract

This paper is concerned with the error and stability analysis of the monotone method for numerical solutions of fourth-order semilinear elliptic boundary value problems. A comparison result among the various monotone sequences is given. The global error is analyzed, and some sufficient conditions are formulated to guarantee a geometric rate of convergence. The stability of the monotone method is proved. Some numerical results are presented.