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Wang, Wan-Sheng; Li, Shou-Fu

On the one-leg \(\theta \)-methods for solving nonlinear neutral functional differential equations. (English) Zbl 1193.34156

Appl. Math. Comput. 193, No. 1, 285-301 (2007).
From the abstract: This paper discusses the one-leg \(\theta \)-methods for the numerical solution of nonlinear neutral functional differential equations with pantograph delay. In recent years, the numerical techniques for the solution to this kind of equations have been developed by numerous authors who have mainly considered the linear system. Instead, in the present paper we study the nonlinear case. The first-step integration of above systems on \([0,T_{0}]\) by one-leg \(\theta \)-methods is analyzed. It is proved that the numerical solution preserves the contractivity property for some \(T_{0}\). On the quasi-geometric mesh, the numerical stability of one-leg \(\theta \)-methods for above systems is investigated. Some sufficient conditions for global stability and asymptotic stability are established. Two numerical examples are also included.

Cited in 46 Documents

MSC:

34K20 Stability theory of functional-differential equations
34K40 Neutral functional-differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations

Keywords:

neutral functional differential equations; nonlinear pantograph delay differential equations; one-leg \(\theta \)-methods; contractivity; numerical stability; quasi-geometric mesh
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References:

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