The aim of this paper is to introduce a new semi-analytical method named precise integration method of lines (PIMOL), which is developed and used to solve the ordinary differential equation (ODE) systems based on the finite difference method of lines and the precise integration method. The irregular domain problem is mainly discussed in this paper. Three classical examples of Poisson’s equation problems are given, including one regular and two irregular domain examples. The PIMOL reduces a semi-discrete ODE problem to a linear algebraic matrix equation and does not require domain mapping for treating the irregular domain problem. Numerical results show that the PIMOL is a powerful method.

本文的目的是介绍一种新的半分析方法，称为线的精确积分方法（PIMOL），该方法用于基于线的有限差分法和精确的方法求解常微分方程（ODE）系统。整合方法。本文主要讨论不规则域问题。给出了泊松方程问题的三个经典例子，包括一个正则和两个不规则域的例子。PIMOL将半离散ODE问题简化为线性代数矩阵方程，并且不需要域映射即可处理不规则域问题。数值结果表明，PIMOL是一种有效的方法。