经典R-K法在扩散方程数值求解中的尝试

扩散方程,通常是带有初值-边值的时倚偏微分方程.通常数值求解这一类偏微分方程是将偏微分方程转化为初值问题的常微分方程,再对常微分方程进行求解.目前的求解方法普遍使用差分法、有限体积法或有限元法来解方程,但在处理实际问题时,这些方法往往因为解的精度不是很理想而使计算结果不合理。本文尝试用经典R-K方法求解扩散方程,并对R-K方法在扩散方程求解中的优点进行简单探讨。

Classic Runge-kutta Methods in Solving Diffusion Equations

Diffusion equations are normally time - dependent partial differential equations with initial value - boundary problems. Normally, the numerical methods for this kind of equations is to convert partial differential equation to initial - value order differential equation, then get the solution of order differential equation. At present, the popular methods are differential methods, infinite volume methods and infinite element methods. But when these methods are used in real situations, the results are unsatisfactory due to poor accuracy. This paper trys using Runge - Kutta(R - K) methods to solve diffusion equtions, and introduces the advantages of Runge - Kutta methods in solving diffusion equations.