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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van der Houwen, P.J., te Riele, H.J.J. Backward differentiation type formulas for Volterra integral equations of the second kind. Numer. Math. 37, 205–217 (1981). https://doi.org/10.1007/BF01398253
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DOI: https://doi.org/10.1007/BF01398253