General linear methods for Volterra integral equations

Authors:
G. Izzo;Z. Jackiewicz;E. Messina;A. Vecchio
Affiliations:
Dipartimento di Matematica e Applicazioni, Universití di Napoli-"Federico II", 80126 Napoli, Italy;Department of Mathematics, Arizona State University, Tempe, AZ 85287, United States and AGH University of Science and Technology, Kraków, Poland;Dipartimento di Matematica e Applicazioni, Universití di Napoli-"Federico II", 80126 Napoli, Italy;IAC-CNR, Via P. Castellino, 111, 80131 Napoli, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 2
Cited 3

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
General Linear Methods for Volterra Integro-differential Equations with Memory

SIAM Journal on Scientific Computing

The short memory principle for solving Abel differential equation of fractional order

Computers & Mathematics with Applications
Highly stable Runge-Kutta methods for Volterra integral equations

Applied Numerical Mathematics
Natural Volterra Runge-Kutta methods

Numerical Algorithms

Quantified Score

Hi-index	7.29

Visualization

Abstract

We investigate the class of general linear methods of order p and stage order q=p for the numerical solution of Volterra integral equations of the second kind. Construction of highly stable methods based on the Schur criterion is described and examples of methods of order one and two which have good stability properties with respect to the basic test equation and the convolution one are given.