New approach to the numerical solution of forward-backward equations

Frontiers of Mathematics in China, 4(1) (2009), 155-168
http://dx.doi.org/10.1007/s11464-009-0006-8

This paper is concerned with the approximate solution of functional differential equations having the form. We search for a solution x, defined for .. 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.