Comparison of Finite-Difference Schemes for the Burgers Problem

Abstract

A large number of problems in physics and engineering leads to boundary value or initial boundary value problems for linear and nonlinear partial differential equations. At the same time, the number of tasks with analytical solutions is limited. These are problems in canonical domains, such as, for example, a rectangle, a circle, or a ball, and usually for equations with constant coefficients. In practice, it is often necessary to solve problems in very complex areas and for equations with variable coefficients, often nonlinear. This leads to the need to search for approximate solutions using various numerical methods.