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Error and stability of monotone method for numerical solutions of fourth-order semilinear elliptic boundary value problems |
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| Authors: | Yuan-Ming Wang |
| Affiliation: | aDepartment of Mathematics, East China Normal University, Shanghai 200062, People's Republic of China bDivision of Computational Science, E-Institute of Shanghai Universities, Shanghai Normal University, Shanghai 200234, People's Republic of China |
| 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. |
| Keywords: | Fourth-order elliptic equations Finite difference solution Monotone method Rate of convergence Global error Stability |
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