Backward differentiation type formulas for Volterra integral equations of the second kind |
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Authors: | P J van der Houwen H J J te Riele |
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Institution: | (1) Stichting Mathematisch Centrum, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands |
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Abstract: | Summary Numerical integration formulas are discussed which are obtained by differentiation of the Volterra integral equation and by applying backward differentiation formulas to the resulting integro-differential equation. In particular, the stability of the method is investigated for a class of convolution kernels. The accuracy and stability behaviour of the method proposed in this paper is compared with that of (i) a block-implicit Runge-Kutta scheme, and (ii) the scheme obtained by applying directly a quadrature rule which is reducible to the backward differentiation formulas. The present method is particularly advantageous in the case of stiff Volterra integral equations. |
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Keywords: | AMS(MOS) 65R20 CR: 5 18 |
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