A ّFast Numerical Method Based on Hybrid Taylor and Block-Pulse Functions for Solving Delay Differential Equations

Document Type : Research Paper


1 Department of Mathematics, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, ‎Iran.

2 Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, ‎Iran.


In this article, a fast numerical approach is proposed for finding the solution of nonlinear delay differential equations by using hybrid Taylor and Block-pulse Functions (HTBPFs). Firstly, some features of hybrid functions which are a combination of Block-Pulse functions and Taylor polynomials on the interval are introduced [0, 1) . In this spectral approach, the operational matrices of stretch, derivation and coefficient matrices are utilized. Based on these piecewise functions, we transfer delay differential equations (DDEs) into a system of linear or nonlinear algebraic equations. Also, in this numerical approach, it is shown that these operational matrices are sparse which is an effective advantage of the fast implementation of numerical computation. Then, error analysis is done. Finally, three examples are solved to show that the new proposed approach is comparable with other methods of high accuracy and efficiency.