非线性发展方程初值问题差分法的收敛判定

A Convergence Criterion for the Difference Method in Initial Value Problem of Nonl.inear Evolution Equation

讨论力学和工程实际应用中经常遇到的一类偏微分方程组—发展方程(或称演变过程方程),并且给出了适定的发展方程初值问题差分解法(仅对时间差分)的收敛估计,本文指出,对一般的、适定的非线性发展方程,如果差分法是相容和稳定的,则差分解一致收敛于原微分方程的真解,因而在三个方面推广了Lax等价定理.

The evoution equation is a system of differential equations often applied in engineering practice and dynamics mechanics theory. In this paper the evolution equation is discussed the convergence estimate for the difference method in the mitial volue problem of evoultion euation is given. The famous has theorem has been developed for solving the linear problem. In this paper, the Lax theorem has been generalized in th? ?spe?ts.