Stability of Runge-Kutta 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:
2002

Citing 4
Cited 13

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Dissipativity of θ-methods for nonlinear Volterra delay-integro-differential equations

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Stability of linear multistep methods for delay integro-differential equations

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Stability properties of second order delay integro-differential equations

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

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Numerical bifurcation analysis of immunological models with time delays

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Dissipativity of one-leg methods for neutral delay integro-differential equations

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High Order Contractive Runge-Kutta Methods for Volterra Functional Differential Equations

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Convergence and stability of extended block boundary value methods for Volterra delay integro-differential equations

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Delay-dependent stability analysis of symmetric boundary value methods for linear delay integro-differential equations

Numerical Algorithms

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Abstract

We study stability of Runge-Kutta (RK) methods for delay integro-differential equations with a constant delay on the basis of the linear equation du/dt = Lu(t) + Mu(t - τ) + K ∫t - τt u(θ)dθ, where L,M,K are constant complex matrices. In particular, we show that the same result as in the case K = 0 (Koto, BIT 34 (1994) 262-267) holds for this test equation, i.e., every A-stable RK method preserves the delay-independent stability of the exact solution whenever a step-size of the form h = τ/m is used, where m is a positive integer.