一类非线性热传导方程的数值解法

The numerical solution to a kind of nonlinear heat conduction equation

研究了一类具有指数型热传导系数的非线性热传导方程,ρCp(■u/■t)=(■/■x)(eku(■u/■x))。在时间方向利用隐式Euler差分格式,空间方向利用二阶中心差分格式,对于离散化后的代数方程组利用Newton迭代法进行求解。通过数值算例分析讨论该方法的合理性和实用性。

This paper studies the nonlinear heat conduction equation with exponential heat transfer coefficient,ρCp(■u/■t)=(■/■x)(eku(■u/■x)).Using the implicit Euler finite difference method in time and two-order center scheme in space,this paper solves the discretized algebraic equations with the Newton iterative method.Finally,the rationality and practice of the method were proved by numerical examples.