子域精细积分及偏微分方程数值解

对于偏微分方程半解析法的方程，精细时程积分虽然能求出高度准确的解，但往往面临矩阵尺度太大的困难；另一方面差分法虽然有带宽小的优点，但有稳定性及精度方面的问题．本文提出子域精细积分法，既可利用精细积分的数值优点，又有带宽小的好处．数值例题表明了子域精细积分法的效能．

Subdomain Precise integration method and numerical solution of partial differential equations

For the semi-analytical method derived equations from the PDEs,the precise integrationmethod can find the highly precise solution,however,it is troublesome when the matrix sizebecomes larger,The usual finite difference method can be executed with a narrow band-width,but faces the problems of numerical stability and precision,Therefore the subdomainprecise integration method is proposed in this paper,it takes both the merits of numericalhigh precision in the subdomain and narrow bandwidth of the matrix. Numerical results showthe benefit of the present methodology.