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Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution 总被引:2,自引:0,他引:2
Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind:
where the solution (t) is assumedto have the form f(t) = x(t)+r?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme. 相似文献
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