Numerical solution for a family of delay functional differential equations using step by step Tau approximations
Journal Title: Bulletin of Computational Applied Mathematics (Bull CompAMa) - Year 2013, Vol 1, Issue 2
Abstract
We use the segmented formulation of the Tau method to approximate the solutions of a family of linear and nonlinear neutral delay differential equations \begin{eqnarray} \nonumber a_1(t)y'(t) & = & y(t)[a_2(t)y(t-\tau)+a_3(t)y'(t-\tau) + a_4(t)] \\ \nonumber & & + \; a_5(t)y(t-\tau) + a_6(t)y'(t-\tau)+ a_7(t), \;\;\; t\geq 0 \\ \nonumber y(t) & = & \Psi(t),\;\;\;\; t\leq 0 \nonumber \end{eqnarray} which represents, for particular values of $a_i(t)$, $i=1,7$, and $\tau$, functional differential equations that arise in a natural way in different areas of applied mathematics. This paper means to highlight the fact that the step by step Tau method is a natural and promising strategy in the numerical solution of functional differential equations.
Authors and Affiliations
René Escalante
Keywords
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