Segmented Tau approximation for a forward-backward functional differential equation

Authors:
Carmen Da Silva;René Escalante
Affiliations:
Departamento de Matemática, Facultad de Ciencias, Universidad Central de Venezuela, Caracas 1020, Venezuela;Departamento de Cómputo Científico y Estadística, División de Ciencias Físicas y Matemáticas, Universidad Simón Bolívar, Ap. 89000, Caracas, 1080-A, Venezue ...
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

A new approach to numerically solve the forward-backward functional differential equation (1)x^'(t)=ax(t)+bx(t-1)+cx(t+1), is presented, where a, b, and c are constant parameters. The step by step version of the Tau method is applied to approximate the solution of Eq. (1) by a piecewise polynomial function. A boundary value problem is posed, solved with the proposed method, and analyzed. The numerical results obtained are consistent with those produced by other methods found in the literature.