二阶弱奇异Volterra积分微分方程的非多项式样条配置方法

Nonpolynomial Spline Collocation Method for Second-Order Volterra Intergro-Differential Equations with Weakly Singular Kernels

研究了二阶弱奇异Volterra积分微分方程的非多项式样条配置,得到了当奇异项指数为有理数时,Volterra积分微分方程解的展开式,由此构造出非多项式样条空间,获得方程在此样条空间中的近似解,并证明了近似解的误差为O(hm).

Nonpolynomial spline collocation method for second-order Volterra intergro-differential equation with weakly singular kernels is considered. When the exponent of the singular item in the equation is a rational number, expansion of the equation＇s solution is obtained. A nonpolynomial spline space is constructed. In the space the approximate solution of the equation is obtained and the order of convergence proved to be O （ h^m）.