zbMATH — the first resource for mathematics

Fast numerical solution of nonlinear Volterra convolution equations. (English) Zbl 0581.65095
Authors’ summary: 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.
Reviewer: J.Albrycht

65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
Full Text: DOI