New approach to the numerical solution of forward-backward equations^?

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.

Keywords

Mixed-type functional differential equations / collocation method / theta-method / method of steps

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