ON THE NUMERICAL SOLUTION OF NEUTRAL DELAY DIFFERENTIAL EQUATIONS USING MULTIQUADRIC APPROXIMATION SCHEME

Title & Authors
ON THE NUMERICAL SOLUTION OF NEUTRAL DELAY DIFFERENTIAL EQUATIONS USING MULTIQUADRIC APPROXIMATION SCHEME
Vanani, Solat Karimi; Aminataei, Azim;

Abstract
In this paper, the aim is to solve the neutral delay differential equations in the following form using multiquadric approximation scheme, (1) $\small{\{_{\;y(t)\;=\;{\phi}(t),\;\;\;\;\;t\;{\leq}\;{t_1},}^{\;y$ where f : $\small{[t_1,\;t_f]\;{\times}\;R\;{\times}\;R\;{\times}\;R\;{\rightarrow}\;R}$ is a smooth function, $\small{\tau(t,\;y(t))}$ and $\small{\sigma(t,\;y(t))}$ are continuous functions on $\small{[t_1,\;t_f]{\times}R}$ such that t-$\small{\tau(t,\;y(t))}$ < $\small{t_f}$ and t - $\small{\sigma(t,\;y(t))}$ < $\small{t_f}$. Also $\small{\phi(t)}$ 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.
Keywords
multiquadric approximation scheme;delay differential equations;neutral delay differential equations;
Language
English
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