Legendre Ritz-Least squares method for the numerical solution of delay differential equations of the multi-pantograph type

Abstract

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.

Keywords

• ‎pantograph equations
• least squares method
• legendre polynomials