Frontiers of Mathematics in China >

2009 , Vol. 4 >Issue 1: 155 - 168

DOI: https://doi.org/10.1007/s11464-009-0006-8

RESEARCH ARTICLE

New approach to the numerical solution of forward-backward equations∗

  • Filomena TEODORO 1,2 ,
  • Pedro M. LIMA , 1 ,
  • Neville J. FORD 3 ,
  • Patricia M. LUMB 3
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  • 1. CEMAT, Instituto Superior Técnico, Lisboa, Portugal
  • 2. EST, Instituto Politécnico de Setúbal, Setúbal, Portugal
  • 3. Department of Mathematics, University of Chester, Chester, UK

Received date: 31 Mar 2008

Accepted date: 13 Nov 2008

Published date: 05 Mar 2009

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

This paper is concerned with the approximate solution of functional differential equations having the form: x′(t)=αx(t)+βx(t-1)+γx(t+1). We search for a solution x, defined for t∈[-1, k], k∈N, which takes given values on intervals [-1, 0] and (k-1, k]. We introduce and analyse some new computational methods for the solution of this problem. Numerical results are presented and compared with the results obtained by other methods.

Key words： Mixed-type functional differential equations; collocation method; theta-method; method of steps

Cite this article

Filomena TEODORO , Pedro M. LIMA , Neville J. FORD , Patricia M. LUMB . New approach to the numerical solution of forward-backward equations∗[J]. Frontiers of Mathematics in China, 2009 , 4(1) : 155 -168 . DOI: 10.1007/s11464-009-0006-8

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