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Fast Numerical Solution of Nonlinear Volterra Convolution Equations

Lubich, Christian
Schlichte, Manfred
Published in SIAM Journal on Scientific and Statistical Computing. 1985, vol. 6, no. 3, p. 532-541
Abstract Numerical methods for general Volterra integral equations of the second kind need O(n^2) kernel evaluations and O(n^2) additions and multiplications. Here it is shown how the effort can be reduced for nonlinear convolution equations. Exploiting the convolution structure, most numerical methods need only O(n) kernel evaluations. With the use of Fast Fourier Transform techniques only O(n(log n)^2) additions and multiplications are necessary. The paper closes with numerical examples and comparisons.
Keywords Volterra integral equationConvolutionFast Fourier transformRunge-Kutta method
Stable URL https://archive-ouverte.unige.ch/unige:12466
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Deposited on : 2010-11-15

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