
New approach to the numerical solution of forward-backward equations
Filomena Teodoro, Pedro M. Lima, Neville J. Ford, Patricia M. Lumb
Front. Math. China ›› 2009, Vol. 4 ›› Issue (1) : 155-168.
New approach to the numerical solution of forward-backward equations
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.
Mixed-type functional differential equations / collocation method / theta-method / method of steps
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