COMPUTER SIMULATION SYSTEM FOR THE NUMERICAL SOLUTION OF THE HEAT EQUATION WITH A POWER-LAW NONLINEARITY BY MESHLESS METHOD

Abstract

The nonlinear parabolic partial differential equations of the second order are the basis of many mathematical models used in physics, mechanics, biology, chemistry, and ecology. For example, the nonlinear heat equation describes the processes of electron and ion thermal conductivity in a plasma, of adiabatic filtration of gases and liquids in porous media, blood flow in capillaries, diffusion of neutrons and alpha particles in reactor materials, chemical kinetics and biological activity. Nonlinear heat conduction processes were first studied by Zel’dovich and Kompaneets The authors considered the process of heat transfer using the mechanism of radiative heat conduction from an instantaneous point source for a one-dimensional problem. The solution to this problem is obtained in an analytical form. The heat equation with a power-law nonlinearity is especially common among the equations of this type. The universal character of this equation makes it possible to assert that the numerical solution of boundary-value problems, which are described by the heat equation withs a power-law nonlinearity, a relevant research. Authors computer simulation the numerical of the one-dimensional nonstationary heat equation a power-law nonlinearity