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http://dx.doi.org/10.4134/BKMS.2008.45.4.663

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

Vanani, Solat Karimi (DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE K. N. TOOSI UNIVERSITY OF TECHNOLOGY)
Aminataei, Azim (DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE K. N. TOOSI UNIVERSITY OF TECHNOLOGY)

Publication Information

Bulletin of the Korean Mathematical Society / v.45, no.4, 2008 , pp. 663-670 More about this Journal

Abstract

In this paper, the aim is to solve the neutral delay differential equations in the following form using multiquadric approximation scheme, (1) $$$\{_{\;y(t)\;=\;{\phi}(t),\;\;\;\;\;t\;{\leq}\;{t_1},}^{\;y$ where f : $[t_1,\;t_f]\;{\times}\;R\;{\times}\;R\;{\times}\;R\;{\rightarrow}\;R$ 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.

Keywords

multiquadric approximation scheme; delay differential equations; neutral delay differential equations;

Citations & Related Records

Times Cited By Web Of Science : 0 (Related Records In Web of Science)
Times Cited By SCOPUS : 4

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