Fast collocation methods for Volterra integral equations of convolution type

Abstract

In this paper we present fast discrete collocation methods for Volterra integral equations of Hammerstein type, where the Laplace transform of the kernel is known a priori. To compute the numerical solution over N t time steps, the constructed methods require O ( N t log ( N t ) ) operations, O ( log ( N t ) ) memory and preserve the order of accuracy of the corresponding exact collocation methods. The numerical experiments confirm the expected accuracy and the computational cost.