Monotone difference schemes of higher accuracy for parabolic equations

Abstract

In this article, monotone difference schemes for linear inhomogeneous parabolic equations, the Fisher or Kolmogorov-Petrovsky-Piskunov equations are constructed and investigated. The stability and convergence of the proposed methods in the uniform norm L ∞  or С is proved. The results obtained are generalized to arbitrary semi-linear parabolic equations with an arbitrary nonlinear sink, as well as to quasi-linear equations.