Monotone Difference Schemes for Convection-Dominated Diffusion-Reaction Equations Based on Quadratic Spline (1712.08560v1)

Abstract: A three-point monotone difference scheme is proposed for solving a one-dimensional non-stationary convection-diffusion-reaction equation with variable coefficients. The scheme is based on a parabolic spline and allows to linearly reproduce the numerical solution of the boundary value problem over the integral segment in the form of the function which continuous with its first derivative. The constructed difference scheme give a highly effective tool for solving problems with a small parameter at the older derivative in a wide range of output data of the problem. In the test case, numerical and exact solutions of the problem are compared with the significant dominance of the convective term of the equation over the diffusion. Numerous calculations showed the high efficiency of the new monotonous scheme developed.