A hybrid collocation method based on combining the third kind Chebyshev polynomials and block-pulse functions for solving higher-order initial value problems

Authors

  • Saeid Jahangiri Dept. of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
  • khosrow maleknejad Islamic Azad University Karaj Branch
  • Majid Tavassoli Kajani

Keywords:

Block-puls functions, collocation method, Chebyshev polynomials, higher-order initial value problems (HOIVPs), hybrid collocation method.

Abstract

The purpose of this paper is to propose a new collocation method for solving linear and nonlinear differential equations of high order as well as solving the differential equation on a very large interval. The new collocation method is based on a hybrid method combining the functions of the third kind Chebyshev polynomials and Block-Pulse functions uses. In the proposed method, the large interval of the problems is divided to small sub-intervals and in each sub-interval, collocation method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution of the differential equation on each sub-intervals. The proposed method is more accurate than the previous methods. Numerical examples show the capability and effciency of the presented method compared to existing methods.

Author Biographies

khosrow maleknejad, Islamic Azad University Karaj Branch

Dept. of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

Majid Tavassoli Kajani

Dept. of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran

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Published

17-11-2016