On Fully Discrete Collocation Methods for Solving Weakly Singular Integro-Differential Equations
Journal Title: Mathematical Modelling and Analysis - Year 2010, Vol 15, Issue 1
Abstract
In order to find approximate solutions of Volterra and Fredholm integrodifferential equations by collocation methods it is necessary to compute certain integrals that determine the required algebraic systems. Those integrals usually can not be computed exactly and if the kernels of the integral operators are not smooth, simple quadrature formula approximations of the integrals do not preserve the convergence rate of the collocation method. In the present paper fully discrete analogs ofcollocation methods where non-smooth integrals are replaced by appropriate quadrature formulas approximations, are considered and corresponding error estimates are derived. Presented numerical examples display that theoretical results are in a good accordance with the actual convergence rates of the proposed algorithms.
Authors and Affiliations
R. Kangro, E. Tamme
Keywords
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- EP ID EP83444
- DOI 10.3846/1392-6292.2010.15.69-82
- Views 94
- Downloads 0
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