A fast iterative method for discretized Volterra-Fredholm integral equations

Authors:
A. Cardone;E. Messina;E. Russo
Affiliations:
Dipartimento di Matematica e Applicazioni, Universití degli Studi di Napoli "Federico II", Via Cintia, I-80126 Napoli, Italy;Dipartimento di Matematica e Applicazioni, Universití degli Studi di Napoli "Federico II", Via Cintia, I-80126 Napoli, Italy;Dipartimento di Matematica e Applicazioni, Universití degli Studi di Napoli "Federico II", Via Cintia, I-80126 Napoli, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 2
Cited 3

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An adaptive method for Volterra-Fredholm integral equations on the half line

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A modified homotopy perturbation method for solving the nonlinear mixed Volterra-Fredholm integral equation

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Abstract

Solving the nonlinear systems arising in the discretization in space and time of Volterra-Fredholm integral equations by Newton iteration leads to dense linear systems whose dimension depends on the spatial mesh. The solution of these linear systems can hence be very costly. Here we try to reduce these costs by solving each Newton iteration by a non-stationary inner iteration process. Each inner iteration again requires the solution of a linear system. However, since the splitting matrix is diagonal, now the components or sets of components can be computed in parallel. The performance of this iteration method is illustrated by means of a few significative examples.