a b s t r a c tThe equations considered in this paper are mixed-type functional equations (sometimes known as forward-backward differential equations) that take the formWe consider basic existence and uniqueness properties when I = [t 1 , t 2 ] and we seekfor prescribed functions w 1 , w 2 absolutely continuous, respectively, on [t 1 − 1, t 1 ], [t 2 , t 2 + 1]. With arbitrary boundary conditions specified in this way, the problem turns out to be ill-posed and so existence and uniqueness questions have an important role to play in developing numerical schemes.We consider, with t 1 , t 2 ∈ N, numerical approximations of a solution when it exists. The numerical methods that we consider are linear θ-methods and we investigate computationally their effectiveness through some illustrative examples.

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This paper is concerned with the approximate solution of functional differential equations having the form: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.

This paper is concerned with the approximate solution of a functional differential equation of the form:(1)We search for a solution x, defined for t ∈ [−1, k],(k ∈ IN), which takes given values on the intervals [−1, 0] and (k − 1, k]. Continuing the work started in [10], we introduce and analyse some new computational methods for the solution of this problem which are applicable both in the case of constant and variable coefficients. Numerical results are presented and compared with the results obtained by other methods.

a b s t r a c tThis paper focuses on the decomposition, by numerical methods, of solutions to mixed-type functional differential equations (MFDEs) into sums of ''forward'' solutions and ''backward'' solutions. We consider equations of the form x (t) = ax(t) + bx(t − 1) + cx(t + 1) and develop a numerical approach, using a central difference approximation, which leads to the desired decomposition and propagation of the solution. We include illustrative examples to demonstrate the success of our method, along with an indication of its current limitations.