一类常微分方程长时间数值计算稳定性分析

摘要

The author considers initial value problem of ording differential equation in the following u′=f(t， .If f(t, u) on u satisfies strong Lip-Condition |f(t, u)-f(t, v)|≤g(t)|u-v|rn u)rn u|=0= u0rnwere non-negative function g(t) satisfies g(t)dt and |g′(t)|dtrn ∫0 ∫0rn un+1--un-1rn bound. Then difference scheme{ 2τ =f (tn, un), n = 1, 2, …rnare( u0=u0, u′=u0+τf (0, u0)rnpossess long time stability and convergence.%考虑如下一类常微分方程初值问题：u′=f(t，u)，u(0)=u0．当函数f(t，u)满足李强朴西兹条件|f(t，u)-f(t，v)≤g(t)|u-v|，其中g(t)满足：∫∞0 g(t)dt，∫∞′(t)|dt有界时，其数值格式：∫ 0 ∫ 0rn un+1-un-1=f(tn,un n=1.2，… / 2τ=f(tn,un)rn u0=u0，u′=u0+τf(0,(0，u0)具有长时间稳定性和收敛性。