两点边值问题基于非均匀网格的高阶紧致差分格式

A High-order Compact Difference Scheme with Non-uniform Grids for Solving the Two-point Boundary Value Problem

在非均匀网格上提出了数值求解两点边值问题的高精度紧致差分格式.首先基于函数的泰勒级数展开,给出了一阶导数和二阶导数在非均匀网格上的差分逼近式;然后结合原模型方程,得到了两点边值问题在非均匀网格上的高精度紧致差分格式,格式具有3-4阶精度;最后,通过数值算例验证了本文格式较文献中已有的格式具有更高的精度和更高的分辨率的优点.

A high-order compact finite difference scheme on the non-uniform grid is proposed to solve the two-point boundary value problem.Based on the Taylor series,the approximate expressions for the first-order and second-order derivatives are constructed.Then a high order compact difference scheme for the two-point boundary value problem is got by using the original equation.At last,the numerical solutions show that the present scheme has many advantages such as more accurate than the existing schemes and higher resolutions.