The Journal of the Australian Mathematical Society Series B Applied Mathematics · 1994 · 28 citations · 15 references
Natural SciencesMathematicsDifferential EquationsConvergence AnalysisFinite Difference MethodsNumerical ConvergenceNumerical Methods For Differential EquationsNumerical StabilityReaction-diffusion SystemsConvergenceFinite Difference DiscretizationFinite Difference SchemesFinite Difference Solution Of Partial Differential EquationsNonlinear Diffusion EquationsReaction-diffusion EquationsStability Of Finite Difference SchemesStability Theorems
Abstract The convergence and stability analysis of a simple explicit finite difference method is studied in this paper. Conditional convergence and stability theorems for this method are given. We have also proved that this scheme is stable in a much stronger sense.
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Difference Methods for Initial-Value Problems
E. I., Robert D. Richtmyer, K. W. Morton · Mathematics of Computation · 1968 · 3.4K citations
<i>Difference Methods for Initial-Value Problems</i>
Robert D. Richtmyer, E. H. Dill · Physics Today · 1959 · 3.2K citations · Full text
<i>Analysis of Numerical Methods</i>
Eugene Isaacson, Herbert B. Keller, George H. Weiss · Physics Today · 1967 · 2.3K citations