On the numerical solution of neutral delay differential equations using multiquadric approximation scheme. (English) Zbl 1168.65039

Summary: In this paper, the aim is to solve the neutral delay differential equations in the following form using multiquadric approximation scheme,
\[ \begin{cases} y'(t) = f(t, y(t), y(t -\tau(t, y(t))), y'(t-\sigma(t, y(t)))),\quad & t_1\leq t\leq t_f,\\ y(t) = \phi(t),& t\leq t_1,\end{cases} \]
where \(f : [t_1, t_f ]\times \mathbb R\times \mathbb R\times \mathbb R\to \mathbb R\) is a smooth function, \(\tau(t, y(t))\) and \(\sigma(t, y(t))\) are continuous functions on \([t_1, t_f ]\times R\) such that \(t-\tau(t, y(t)) < t_f\) and \(t-\sigma(t, y(t)) < t_f\) . Also \(\phi(t)\) represents the initial function or the initial data. Hence, we present the advantage of using the multiquadric approximation scheme. In the sequel, presented numerical solutions of some experiments, illustrate the high accuracy and the efficiency of the proposed method even where the data points are scattered.


65L05 Numerical methods for initial value problems involving ordinary differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
34K40 Neutral functional-differential equations
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