Stability of θ-methods for delay integro-differential equations

Authors:
Toshiyuki Koto
Affiliations:
Department of Computer Science, The University of Electro-Communications, Tokyo 182-8585, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

Citing 7
Cited 6

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Numerical stability of the &thgr;-methods for systems of differential equations with several delay terms

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Stability properties of a scheme for the approximate solution of a delay-integro-differential equation

Selected papers from the international conference on Numerical solution of Volterra and delay equations
On the &thgr;-method for delay differential equations with infinite lag

Journal of Computational and Applied Mathematics
Retarded differential equations

Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Stability of Runge-Kutta methods for delay integro-differential equations

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Dissipativity of linear θ-methods for integro-differential equations

Computers & Mathematics with Applications
Dissipativity of θ-methods for nonlinear Volterra delay-integro-differential equations

Journal of Computational and Applied Mathematics
Stability of linear multistep methods for delay integro-differential equations

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Stability of Runge-Kutta methods for neutral delay-integro-differential-algebraic system

Mathematics and Computers in Simulation
Errors of linear multistep methods for singularly perturbed Volterra delay-integro-differential equations

Mathematics and Computers in Simulation
Delay-dependent stability analysis of symmetric boundary value methods for linear delay integro-differential equations

Numerical Algorithms

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Abstract

Stability of θ-methods for delay integro-differential equations (DIDEs) is studied on the basis of the linear equation du/dt= λu(t) + µu(t - τ) + k ∫t-τt u(σ) dσ, where λ,µ,k are complex numbers and τ is a constant delay. It is shown that every A-stable θ-method possesses a similar stability property to P-stability, i.e., the method preserves the delay-independent stability of the exact solution under the condition that k is real and τ/h is an integer, where h is a step-size. It is also shown that the method does not possess the same property if τ/h is not an integer. As a result, no θ-method can possess a similar stability property to GP-stability with respect to DIDEs.