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Product integration for weakly singular integro-differential equations

    Arvet Pedas Affiliation
    ; Enn Tamme Affiliation

Abstract

On the basis of product integration techniques a discrete version of a piecewise polynomial collocation method for the numerical solution of initial or boundary value problems of linear Fredholm integro-differential equations with weakly singular kernels is constructed. Using an integral equation reformulation and special graded grids, optimal global convergence estimates are derived. For special values of parameters an improvement of the convergence rate of elaborated numerical schemes is established. Presented numerical examples display that theoretical results are in good accordance with actual convergence rates of proposed algorithms.

Keyword : weakly singular integro-differential equation, collocation method, product integration, graded grid

How to Cite
Pedas, A., & Tamme, E. (2011). Product integration for weakly singular integro-differential equations. Mathematical Modelling and Analysis, 16(1), 153-172. https://doi.org/10.3846/13926292.2011.564771
Published in Issue
Apr 8, 2011
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