Numerical Method for Solving the Reaction-Diffusion Equation
DOI:
https://doi.org/10.52575/2687-0959-2025-57-1-52-58Keywords:
Reaction-Diffusion Equation, Fisher Equation, KPP Equation, Difference Scheme, Weighted Scheme, Finite Fifference Approximation, Computational ExperimentAbstract
Mathematical models with this equation are widely used in ecology, physiology, combustion, crystallization, plasma physics, and in general phase transition problems. In this article, we are interested in the finite-difference approximation of the initial-boundary value problem with the KPP-F equation. For this, a two-layer difference scheme "with weights" was built, having an approximation order of O(h2 + τ). The used scheme made it possible to reduce the problem of finding a solution to a nonlinear equation to solving a system of linear algebraic equations using the sweep method. If
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