具非线性对流项热传导方程的有限差分法

Study on Finite Difference Method of Heat Conduction Equation with Nonlinear Convection Term

给出了具非线性对流项热传导方程的有限差分法,利用Matlab软件结合有限差分法,针对具体的算例,得出相应的数值解,并与真实解进行比较.重点探讨了当方程中指数参数发生变化时,相应的数值差分解是否会发生改变的情况.发现参数不宜取得过小,否则可能会导致数值结果不稳定.

The finite difference method of heat conduction equation with nonlinear convection term is presented.Through the combination of Matlab software and the finite difference method,the numerical solution is obtained and compared with the exact solution.This paper mainly discusses whether the corresponding numerical difference solution will change when the exponential parameter changes.It is found that the parameter should not be too small.Otherwise the numerical results may be unstable.