• Title, Summary, Keyword: multiquadric approximation scheme

Search Result 1, Processing Time 0.019 seconds

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

  • Vanani, Solat Karimi;Aminataei, Azim
    • Bulletin of the Korean Mathematical Society
    • /
    • v.45 no.4
    • /
    • pp.663-670
    • /
    • 2008
  • In this paper, the aim is to solve the neutral delay differential equations in the following form using multiquadric approximation scheme, (1) $$\{_{\;y(t)\;=\;{\phi}(t),\;\;\;\;\;t\;{\leq}\;{t_1},}^{\;y'(t)\;=\;f(t,\;y(t),\;y(t\;-\;{\tau}(t,\;y(t))),\;y'(t\;-\;{\sigma}(t,\;y(t)))),\;{t_1}\;{\leq}\;t\;{\leq}\;{t_f},}$$ 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.