New approach to the numerical solution of forward-backward equations |
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Authors: | Filomena Teodoro Pedro M. Lima Neville J. Ford Patricia M. Lumb |
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Affiliation: | (1) CEMAT, Instituto Superior Técnico, Lisboa, Portugal;(2) EST, Instituto Politécnico de Setúbal, Setúbal, Portugal;(3) Department of Mathematics, University of Chester, Chester, UK |
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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. |
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Keywords: | Mixed-type functional differential equations collocation method theta-method method of steps |
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