SIAM Journal on Scientific and Statistical Computing
Convolution quadrature and discretized operational calculus I.
Numerische Mathematik
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Fast Convolution for Nonreflecting Boundary Conditions
SIAM Journal on Scientific Computing
Multistep collocation methods for Volterra Integral Equations
Applied Numerical Mathematics
Two-step diagonally-implicit collocation based methods for Volterra Integral Equations
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
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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 Nt time steps, the constructed methods require O(Nt log(Nt)) operations, O(log(Nt)) memory and preserve the order of accuracy of the corresponding exact collocation methods. The numerical experiments confirm the expected accuracy and the computational cost.