Numerical solution of weakly singular Volterra integro-differential equations with change of variables

Authors:
Marek Kolk;Arvet Pedas
Affiliations:
Institute of Applied Mathematics, University of Tartu, Tartu, Estonia;Institute of Applied Mathematics, University of Tartu, Tartu, Estonia
Venue:
ICOSSE'06 Proceedings of the 5th WSEAS international conference on System science and simulation in engineering
Year:
2006

Citing 4
Cited 0

High order methods for weakly singular integral equations with nonsmooth input functions

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Variable transformations in the numerical solution of second kind Volterra integral equations with continuous and weakly singular kernels; extensions to Fredholm integral equations

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Piecewise Polynomial Collocation Methods for Linear Volterra Integro-Differential Equations with Weakly Singular Kernels

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A new approach to the numerical solution of weakly singular Volterra integral equations

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Abstract

We discuss a possibility to construct high order methods on uniform or mildly graded grids for the numerical solution of linear Volterra integro-differential equations with weakly singular or other nonsmooth kernels. Using an integral equation reformulation of the initial value problem, we apply to it a smoothing transformation so that the exact solution of the resulting equation does not contain any singularities in its derivatives up to a certain order. After that the regularized equation is solved by a piecewise polynomial collocation method on a mildly graded or uniform grid. In particular, a numerical method based on the Haar wavelets can be constructed.