Numerical integration of one-dimensioned parabolic problems using adaptive grids

A method of numerical integration of one-dimensioned parabolic initial boundary value problems with contrast structures using movable adaptive grids is described. A difference scheme which is resistant to machine rounding errors and time-monotonic is constructed. Algorithms for constructing adaptive grids in space and time are proposed. A series of numerical experiments using the example of a singularly perturbed “reaction-diffusion-advection” problem is provided.