Numerical Modelling of a Functional Differential Equation with Deviating Arguments Using a Collocation Method

This paper is concerned with the approximate solution of a functional differential equation of the form: x'(t) α(t)x(t)+β(t)x(t-1)+γ(t)x(t+1). We search for a solution x, defined for t(set-membership sign)[-1,k],(k(set-membership sign)N), which takes given values onn the intervals [-1,0] and (k-1,k]. Continuing the work started in [10], we introduce and anlyse 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.