一类非线性发展方程的交替方向格式

对一类非线性发展方程使用一种变换,通过增加人工扰动项,得到了算子乘积型的有限差分格式.利用算子分裂可实现新型Douglas形式的交替方向差分格式,并实现了交替方向求解,这样可以把高维问题化成若干个独立的一维问题逐次求解,大大降低了计算量.本文应用向量积计算及先验估计理论和技巧,得到最佳的L2模误差估计.数值试验表明了所提格式的稳定性和有效性,以及理论分析的正确性.

The Alternating Direction Scheme for a Kind of Nonlinear Evolution Equation

A class of nonlinear evolution equations are concerned in this paper.By using a transformation and adding a perturbation term,we obtain a difference scheme of operator times type.Using operator splitting method,we can get a alternating direction difference of new Douglus type of scheme,and solve the problem using alternating direction method,This yields the multidimensional difference system that are decomposed to sets of independent one-dimensional problems.Calculation efficiency is improved greatly.It is shown that the scheme is second-order accurate in time and in space in the H-norm.Using the calculation of vector product and the theory and technique of priori estimate, optimal order error estimates in L~2 is obtained.Numerical result implies the theoretical analysis are correct and the scheme are effective.