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.
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