一类演化方程的高稳定性的差分格式

THE DIFFERENCE SCHEMES WITH HIGHER STABILITY PROPERTIES FOR A CLASS OF EVOLUTION EQUATION

摘要: 考虑一类演化方程u_t=au∂_2k+1(其中a是常数,u∂_2k+1=∂^2k+1u/∂x^2k+1,k=1,2……)的有限差分解法。构造了两类具有高稳定性的显式差分格式。并用引入耗散项的方法建立了两类半显式差分格式,它们是无条件稳定的且可显式地进行计算。

Abstract: In order to solve a class of evolution equaiton u_t=au2K+1(where a is constant, u_2K+1=∂^2K+1/∂x_2K+1,K=l,2,……) two classes of explicit difference schemes with higher stability properties are constituted. And two classes of semi -explicit difference schemes are also established by introducing a dissipative term, they are unconditionally stable and can be calculated explicitly.