论文标题
一种有效的光谱方法，用于用非平滑溶液求解第三种Volterra积分方程
An efficient spectral method for solving third-kind Volterra integral equations with non-smooth solutions
论文作者
论文摘要
本文与基于光谱tau方法的递归方法的第三类伏尔特拉积分方程的数值解有关。为此，介绍了一组新的分数版本的分数版本多项式（称为FC-多项式）。近似多项式溶液（称为tau-solution）用FC多项式表示。 Tau-soluste的分数结构即使在非平滑溶液的情况下，也可以恢复光谱方法的标准准确性。研究了该方法的收敛分析。获得的数值结果表明，与其他现有方法相比，该方法的准确性和效率。
This paper is concerned with the numerical solution of the third kind Volterra integral equations with non-smooth solutions based on the recursive approach of the spectral Tau method. To this end, a new set of the fractional version of canonical basis polynomials (called FC-polynomials) is introduced. The approximate polynomial solution (called Tau-solution) is expressed in terms of FC-polynomials. The fractional structure of Tau-solution allows recovering the standard degree of accuracy of spectral methods even in the case of non-smooth solutions. The convergence analysis of the method is studied. The obtained numerical results show the accuracy and efficiency of the method compared to other existing methods.
