Monotone Finite Difference Schemes for Nonlinear Systems with Mixed Quasi-Monotonicity |
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Authors: | Yuan-ming Wang Ben-yu Guo |
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Institution: | a Department of Mathematics, East China Normal University, Shanghai, 200062, People's Republic of Chinab Department of Mathematics, Shanghai Normal University, Shanghai, 200234, People's Republic of China |
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Abstract: | Monotone finite difference schemes are proposed for nonlinear systems with mixed quasi-monotonicity. Two monotone iteration processes for the corresponding discrete problems are presented, which converge monotonically to the quasi-solutions of the discrete problems. The limits are the exact solutions under some conditions. A monotone finite difference scheme on uniform mesh with the accuracy of fourth order is constructed. The numerical results coincide with theoretical analysis. |
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Keywords: | nonlinear systems mixed quasi-monotonicity monotone finite difference method accuracy of fourth order |
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