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The approximate solution of initial-value problems for general Volterra integro-differential equations. (English) Zbl 0631.65141
We study the application of certain polynomial spline collocation methods to Volterra integrodifferential equations of order r where the rth derivative of the unknown solution occurs also in the kernel function of the equation. The analysis focuses on the questions of the attainable order of discrete (local) convergence and the numerical implementation of these methods. The performance of the resulting implicit Runge-Kutta- Nyström type methods is illustrated by numerical examples.

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
Full Text: DOI
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