Numerical solution for a family of delay functional differential equations using step by step Tau approximations

• Main Author: René Escalante
• Format: Article
• Language: English
• Published: Universidad Simón Bolívar 2013-12-01
• Series: Bulletin of Computational Applied Mathematics
• Subjects: Alternating generalized projection method; method of generalized projection; method of alternating projection; error sums of distances; product vector space; feasible solution; trap points; intersection of sets
• Online Access: http://drive.google.com/open?id=0B5GyVVQ6O030TlY5bzFScENubUU

We use the segmented formulation of the Tau method to approximate the solutions of a family of linear and nonlinear neutral delay differential equations a₁(t) y'(t) = y(t)[a₂(t)] y(t-τ) + a₃(t) y'(t-τ) + a₄(t)] + a₅(t) y(t-τ) + a₆(t) y'(t-τ) + a₇(t), t ≥ 0 y(t) = Ψ(t), t ≤ 0 which represents, for particular values of a_i(t), i=1,7, and τ, 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.