Partial differential equation calculation and visualization

Abstract

The calculation of partial differential equations has wide applied background. Many of the problems in scientific research and engineering can be the mathematical model of partial differential equations. Differential equation containing multiple independent variables is called as PDE (partial differential equation). As for PDE problem, it is very difficult to solve. Apart from a few special cases, the vast majority of cases are difficult to obtain exact solutions. For the majority of applications workers, from the point of partial differential equations, using the finite element method or finite difference method has to spend a lot of effort to get numerical solution. By MATLAB PDEToolbox, the article introduced the accurate solution process of two-dimensional problem with high-speed. In order to see the relationship between graph, function value and independent variable from the mathematical expression of partial differential equations by MATLAB programming, numerical solution, and the results can be visualized. PDE Toolbox provides a powerful and flexible as well as practical environment for research and problem solving about partial differential equations in two-dimensional space.

Keywords:

• Partial differential equations
• Difference method
• Spectral method
• MATLAB