On the numerical solution of neutral delay differential equations using multiquadric approximation scheme

Bull. Korean Math. Soc. 2008 Vol. 45, No. 4, 663-670 Printed December 1, 2008

Solat Karimi Vanani and Azim Aminataei K. N. Toosi University of Technology

Abstract : In this paper, the aim is to solve the neutral delay differential equations in the following form using multiquadric approximation scheme, \begin{equation}
\left\lbrace
\begin{array}{l }
y'(t)=f(t,y(t),y(t-\tau(t,y(t))),y'(t-\sigma(t,y(t)))),\hspace{.15cm} t_{1} \leq t \leq t_{f},\\
y(t)=\phi(t),\hspace{.5cm}t \leq t_{1},
\end{array}
\right.
\end{equation} 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))