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

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）.