General Linear Methods for Volterra Integro-differential Equations with Memory

Authors:
Chengjian Zhang;Stefan Vandewalle
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2005

Citing 0
Cited 7

The extended one-leg methods for nonlinear neutral delay-integro-differential equations

Applied Numerical Mathematics
Recent advances in the numerical analysis of Volterra functional differential equations with variable delays

Journal of Computational and Applied Mathematics
General linear methods for Volterra integral equations

Journal of Computational and Applied Mathematics
Dissipativity of one-leg methods for neutral delay integro-differential equations

Journal of Computational and Applied Mathematics
High Order Contractive Runge-Kutta Methods for Volterra Functional Differential Equations

SIAM Journal on Numerical Analysis
Convergence and stability of extended block boundary value methods for Volterra delay integro-differential equations

Applied Numerical Mathematics
Original article: Nonlinear stability of one-leg methods for neutral Volterra delay-integro-differential equations

Mathematics and Computers in Simulation

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Abstract

A new class of numerical methods for Volterra integro-differential equations with memory is developed. The methods are based on the combination of general linear methods with compound quadrature rules. Sufficient conditions that guarantee global and asymptotic stability of the solution of the differential equation and its numerical approximation are established. Numerical examples illustrate the convergence and effectiveness of the numerical methods.