Improved Difference Scheme for a Singularly Perturbed Parabolic Reaction-Diffusion Equation with Discontinuous Initial Condition
A Dirichlet problem is considered for a singularly perturbed parabolic reaction-diffusion equation with a piecewise-continuous initial condition. For this problem, using the method of additive splitting of singularities (generated by discontinuities of the initial function and its lowest derivatives) and the Richardson method, a finite difference scheme on piecewise-uniform meshes is constructed that converges ε-uniformly with the third and second order of accuracy in x and t, respectively.
KeywordsInitial Function Singular Component Grid Approximation Additive Splitting Richardson Scheme
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