A numerical method based on Legendre differentiation matrices for higher order ODEs

Authors

M. Abdelhakem, Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt\\ Canadian International College, School of Engineering, Basic Science Department, Cairo, EgyptFollow
M. Biomy, Department of Mathematics, Faculty of Science, Suez Canal University, Port-Said, Egypt\\Department of Mathematics, College Of Sciences and Arts, Al-Ras, Al-Qassim University, KSAFollow
S. A. Kandil, Canadian International College, School of Engineering, Basic Science Department, Cairo, EgyptFollow
D. Baleanu, Department of Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey\\Institute of Space Sciences, Magurele-Bucharest, RomaniaFollow

Abstract

This paper introduces a new method to obtain the spectral accuracy solutions to higher order differential equations and singularly perturbed boundary value problems (BVPs). Legendre polynomials (LPs) Pn(x) have been used and involved in straightforward implementation method. Asymptotic upper bound on the Legendre coefficients for the kth derivatives are presented. Also, We detect the roundoff error effect in the Legendre matrices. The superiority of the suggested method became evident through some examples and applications.

Recommended Citation

Abdelhakem, M.; Biomy, M.; A. Kandil, S.; and Baleanu, D. (2020) "A numerical method based on Legendre differentiation matrices for higher order ODEs," Information Sciences Letters: Vol. 9 : Iss. 3 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol9/iss3/3