A new exponential Chebyshev operational matrix of derivatives for solving high-order ordinary differential equations in unbounded domains

Journal of Modern Methods in Numerical Mathematics

Kamal Raslan¹  Mohamed A. Abd Elsalam¹  Talaat El Danaf³  Mohamed Ramadan² 

[1] Al-Azhar University;Menoufia University;Taibah University

关键词: Contraception;    Family planning;    Under-five mortality;    Unmet need;    Nigeria;   

DOI  :  10.20454/jmmnm.2016.1068

学科分类：社会科学、人文和艺术（综合）

来源: Modern Science Publishers

【 摘 要 】

The purpose of this paper is to investigate a new exponential Chebyshev (EC) operational matrix of derivatives. The new operational matrix of derivatives of the EC functions is derived and introduced for solving high-order linear ordinary differential equations with variable coefficients in unbounded domain using the collocation method. This method transforms the given differential equation and conditions to matrix equation with unknown EC coefficients. These matrices together with the collocation method are utilized to reduce the solution of high-order ordinary differential equations to the solution of a system of algebraic equations. The solution is obtained in terms of EC functions. Numerical examples are given to demonstrate the validity and applicability of the method. The obtained numerical results are compared with others existing methods and the exact solution where it shown to be very attractive with good accuracy.

【 授权许可】

Unknown