一类奇异微分方程边值问题的数值方法

Numerical Method for a Class of Singular Boundary Value Problems of Differential Equations

在再生核空间中讨论一类二阶奇异微分方程两点边值问题.研究方程解存在的充分性和解唯一的必要性,建立解的精确表达式,获得近似解的求解方法,数值模拟结果说明该方法的有效性.

In this paper, a class of singular two - point boundary value problems （BVPs） of second - order ordinary differential equations in the reproducing kernel space is discussed . A sufficient condition which guarantee the existence of solution is discussed and a necessary condition for uniqueness of solution is established . Moreover, the exact representation of the solution of the singular BVPs is presented and a algorithm is given to solve this kind of equations. The numerical experiments are displayed to demonstrate the validity of the method.