Numerical Methods for Partial Differential Equations · 2003 · 43 citations · 4 references
Natural SciencesComputational EngineeringComputational Fluid DynamicsComputational MechanicsDifferential EquationsConvergence AnalysisFinite Difference MethodsNumerical ConvergenceNumerical Methods For Differential EquationsPartial Differential EquationsReaction-diffusion SystemsDiscretization Error AnalysisFinite Difference DiscretizationFinite Difference SchemesFinite Difference Solution Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsReaction-diffusion EquationsStability Of Finite Difference Schemes
Abstract A competitive nonstandard semi‐explicit finite‐difference method is constructed and used to obtain numerical solutions of the diffusion‐free generalized Nagumo equation. Qualitative stability analysis and numerical simulations show that this scheme is more robust in comparison to some standard explicit methods such as forward Euler and the fourth‐order Runge‐Kutta method (RK4). The nonstandard scheme is extended to construct a semi‐explicit and an implicit scheme to solve the full Nagumo reaction‐diffusion equation. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 363–379, 2003.
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An introduction to chaotic dynamical systems
Acta Applicandae Mathematicae · 1990 · 1.6K citations · Full text