Soution of convection-diffusion equations

Abstract

Partial differential equations are an important part of mathematics in science and its numerical solution occupies an important position in the numerical analysis. Partial differential equations are closely related to human life and it has important research value. At present, people have studied its solutions in depths and achieved a lot of valuable results. The current solution is the finite element method and finite different method. The convection-diffusion equation is more closely related to human activities, especially complex physical processes. The behavior of many parameters in flow phenomena follows the convection-diffusion equation, such as momentum and heat. The convection-diffusion equation is also used to describe the diffusion process in environmental science, such as the pollutant transport in the atmosphere, oceans, lakes, rivers or groundwater. The research of the convection-diffusion equation is of great importance. Partial differential equation theory has important applications in the solution of the convection-diffusion equation. This chapter mainly talks about the application of the finite difference method in the solution of the convection-diffusion equation. © Springer-Verlag Berlin Heidelberg 2013.