Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels

F. C. Hoppensteadt; Zdzislaw Jackiewicz; B. Zubik-Kowal

doi:10.1007/s10543-007-0122-3

Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels

F. C. Hoppensteadt, Zdzislaw Jackiewicz, B. Zubik-Kowal

CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

Variable stepsize algorithms for the numerical solution of nonlinear Volterra integral and integro-differential equations of convolution type are described. These algorithms are based on an embedded pair of Runge-Kutta methods of order p=5 and p=4 proposed by Dormand and Prince with interpolation of uniform order p=4. They require O(N) number of kernel evaluations, where N is the number of steps. The cost of the algorithms can be further reduced for equations that have rapidly vanishing convolution kernels, by using waveform relaxation iterations after computing the numerical approximation by variable stepsize algorithm on some initial interval.

Original language	English (US)
Pages (from-to)	325-350
Number of pages	26
Journal	BIT Numerical Mathematics
Volume	47
Issue number	2
DOIs	https://doi.org/10.1007/s10543-007-0122-3
State	Published - Jun 1 2007

Keywords

Embedded Runge-Kutta methods
Numerical simulation of linear and nonlinear time invariant systems
Volterra integral equation of convolution type
Waveform relaxation iterations

ASJC Scopus subject areas

Software
Computer Networks and Communications
Computational Mathematics
Applied Mathematics

Access to Document

10.1007/s10543-007-0122-3

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