求解扩散方程的二级四阶隐式 Runge-Kutta 方法

摘要

We applieed central finite difference approximation of second order and compact finite difference approximation of fourth order for discrediting spatial derivatives ,and used two stage fourth order Runge-Kutta method in time direction derived two unconditionally stable implicit schemes in which local truncation error was O(τ4 + h2 ) and O(τ4 + h4 ) ,then discussed its stability .Numerical experiment was compared with Crank-Nicolson scheme .Numerical experiment results showed that it was an efficient method for solving diffusion equation .%对空间变量应用中心差分格式和紧致差分格式离散，时间变量采用二级四阶 Runge-Kutta方法，构造求解扩散方程的精度为O（τ4＋ h2）和 O（τ4＋ h4）的两种绝对稳定的隐式差分格式，讨论稳定性，并将数值试验结果与Crank-Nicholson格式进行比较，数值结果表明该方法是求解扩散方程的有效数值计算方法之一。