Block boundary value methods for solving linear neutral Volterra integro-differential equations with weakly singular kernels
Stynes, Martin 1Zhou, Yongtao1
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作者信息
1. Beijing Computat Sci Res Ctr
折叠
Abstract
A class of block boundary value methods is constructed for the solution of linear neutral Volterra integro-differential equations with weakly singular kernels. Under suitable conditions on the data, it is shown that these methods yield optimal convergence rates when implemented on special graded meshes. Furthermore, these methods are easily extended to solve linear Volterra integral equations of the 2nd kind with weakly singular kernels. Numerical experiments confirm the theoretical results and the accuracy of the methods, and a comparison with piecewise polynomial collocation methods is provided. (C) 2021 Elsevier B.V. All rights reserved.
Key words
Block boundary value methods/Linear neutral Volterra integro-differential equations/Linear Volterra integral equations/Weakly singular kernel/Graded mesh/Ordinary differential equations/SPLINE COLLOCATION METHODS/CONVERGENCE/STABILITY/MULTISTEP
NSTL
Elsevier