legendre ritz-least squares method for the numerical solution of delay differential equations of the multi-pantograph type

This paper is concerned with a legendre ritz-least squares technique for the non-singular and singular delay differential equations (ddes) of multi-pantograph type. this tech-nique is based on legendre polynomials and least squares. the legendre ritz-least squarestechnique (lrls) is used to decrease the problem to a set of the algebraic equation system.the efficiency and reliability of the proposed method are shown by some numerical results. allof the numerical implementations have been performed on a pc using some programs written inmathematica.