一类非均匀网格有限差分方法稳定性和数值解唯一性研究

Uniqueness and stability study of a kind of finite difference scheme with non-uniform meshes

本文针对半线性抛物方程的一类全隐非均匀网格差分格式研究了它的稳定性及其数值解的唯一性,证明方法是离解能量模范数.分析表明,其数值解在L∞和L2意义下收敛阶为O(τ+h).通过恰当的实验设计完成数值实验,作者验证了理论分析的正确性.

In this paper,uniqueness and stability are proved complementally for a kind of implicit difference scheme on non-uniform meshes.The proof method is discrete energy normal method.Meanwhile,numerical experiments are carried out to justify the theoretical analyses,which the convergence degree is O（τ＋h） in both discrete norm L∞ and L2,rescpectively.By appropriate numberical experiments it is concluded that theoretical analyses are correct.