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A Stable Numerical Approach for Implicit Non-Linear Neutral Delay Differential Equations
Authors:R Vermiglio  L Torelli
Institution:(1) Dipartimento di Matematica e Informatica, Università di Udine, I-33100 Udine, Italy;(2) Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, I-34100 Trieste, Italy
Abstract:In this paper we consider implicit non-linear neutral delay differential equations to derive efficient numerical schemes with good stability properties. The basic idea is to reformulate the original problem eliminating the dependence on the derivative of the solution in the past values. Our hypothesis on the original equation allow us to study the boundedness and asymptotic stability of the true and numerical solutions by the theory of stability with respect to the forcing term.
Keywords:Neutral delay differential equations  Runge–  Kutta methods  stability analysis
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