Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels |
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| Authors: | FC Hoppensteadt Z Jackiewicz B Zubik-Kowal |
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| Institution: | (1) Councelor to the Provost, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St. , New York, NY 10012, USA;(2) Department of Mathematics, Arizona State University, Tempe, AZ 85287, USA;(3) Department of Mathematics, Boise State University, 1910 University Drive, Boise, ID 83725, USA |
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| 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.
AMS subject classification (2000) 65R20, 45L10, 93C22 |
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| Keywords: | Volterra integral equation of convolution type embedded Runge– Kutta methods numerical simulation of linear and nonlinear time invariant systems waveform relaxation iterations |
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