Numerical solving of partial differential equations with heredity and nonlinearity in the differential operator

Abstract

The problem to be considered is a numerical solving of nonlinear partial differential equations with heredity effect. Nonlinearity is contained in the operator of differentiation as well as in the inhomogeneity function. We propose a nonlinear implicit difference scheme, which implies the use of iterative methods to find the solution on each time layer. To take into account the heredity effect the interpolation and extrapolation of grid solution were used. Stability and convergence of the proposed difference scheme were proved. Numerical experiments were carried out and results coincides with the theoretical ones.