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
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摘要: 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).Abstract: 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（hm）.
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