Comparative Analysis of Schemes with Movable Nodes for a Parabolic Equation

Abstract

The article considers an approximate analytical solution of a linear parabolic equation with initial and boundary conditions. Many problems in engineering applications are reduced to solving an initial-boundary value problem of parabolic type. There are various analytical, approximate-analytical and numerical methods for solving such problems. The most popular difference methods for solving an initial-boundary value problem of a parabolic equation are explicit, implicit and Crank-Nicolson schemes. Here, we consider methods for obtaining an approximate-analytical solution based on the movable node method and their comparative analysis of these schemes for specific test problems. A comparison of the exact and approximate solutions is made using specific examples.