Cubic spline as global approximate solution of the semilinear reaction--diffusion problem
Keywords:Singular perturbation, nonlinear, boundary layer, cubic spline, equidistant mesh, Shishkin mesh
In this paper we consider the semilinear singularly perturbed reaction--diffusion boundary value problem. In the first part of the paper a difference scheme is given for the considered problem. In the main part of the paper a cubic spline is constructed and we show that it represents a global approximate solution of the our problem. At the end of the paper numerical examples are given, which confirm the theoretical results.
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