Abstract
This paper is concerned with the numerical stability of a class of nonlinear neutral delay differential equations. The numerical stability results are obtained for(k,l)-algebraically stable Runge-Kutta methods when they are applied to this type of problem. Numerical examples are given to confirm our theoretical results.
Highlights
Let ⟨⋅, ⋅⟩ be an inner product on CN and let ‖ ⋅ ‖ be the corresponding norm
Y (t) = φ (t), − τ ≤ t ≤ 0, and they obtained a series of stability results of theoretical solution and numerical solution which was given by backward Euler methods
In 2012, the authors of the present paper considered problem (1), and a sufficient condition for the stability of the problem itself is given [1]
Summary
Let ⟨⋅, ⋅⟩ be an inner product on CN and let ‖ ⋅ ‖ be the corresponding norm. Consider the initial value problems (IVPs) of nonlinear neutral delay differential equations (NDDEs) as follows (cf. [1]): y (t) = f (t, y (t) , y (t − τ1) , y (t − τ2)) , t ≥ t0, (1). Y (t) = φ (t) , − τ ≤ t ≤ 0, and they obtained a series of stability results of theoretical solution and numerical solution which was given by backward Euler methods They further investigated the stability of one-leg methods [5], Runge-Kutta methods [6], and continuous Runge-Kutta-type methods [7] for the solution to problem (8), respectively. In 2012, the authors of the present paper considered problem (1), and a sufficient condition for the stability of the problem itself is given [1] In [1], the numerical stability results are obtained for A-stable one-leg methods when they are applied to problem (1) This paper pursues this and further investigates the stability of Runge-Kutta methods for problem (1).
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