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

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.

Keywords

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