Modified Finite Integration Method Using Chebyshev Polynomial for Solving Linear Differential Equations

R. Boonklurb1, A. Duangpan2 and T. Treeyaprasert3
1,2Department of Mathematics and Computer Science, Faculty of Science,
Chulalongkorn University, Bangkok 10330, Thailand
3Department of Mathematics and Statistics, Thammasat University,
Rangsit Center, Pathumthani 12120, Thailand

Received 10 January 2018; accepted in revised form 27 August 2018

Abstract: We propose a modified finite integration method (FIM) by using the Chebyshev polynomial, to construct the first order integral matrix for solving linear differential equations in one and two dimensions. The grid points for the computation are generated by the zeros of the Chebyshev polynomial of a certain degree. We implement our method with several examples arose from real-world applications. In comparison with the finite difference method and the traditional FIMs (trapezoidal and Simpson’s rules), numerical computations show that our modified FIM using Chebyshev nodes require the less computational cost to achieve significant improvement in accuracy.

c 2018 European Society of Computational Methods in Sciences and Engineering
Keywords: Finite integration method, Linear di fferential equations, Chebyshev polynomial.
Mathematics Subject Classi cation: 65L05, 65L10, 65N30

 

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