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- Title
Harmonic numbers operational matrix for solving fifth-order two point boundary value problems.
- Authors
Youssri, Y. H.; Abd-Elhameed, W. M.
- Abstract
The principal purpose of this paper is to present and implement two numerical algorithms for solving linear and nonlinear fifth-order two point boundary value problems. These algorithms are developed via establishing a new Galerkin operational matrix of derivatives. The nonzero elements of the derived operational matrix are expressed explicitly in terms of the well-known harmonic numbers. The key idea for the two proposed numerical algorithms is based on converting the linear or nonlinear fifth-order two BVPs into systems of linear or nonlinear algebraic equations by employing Petrov-Galerkin or collocation spectral methods. Numerical tests are presented aiming to ascertain the high effciency and accuracy of the two proposed algorithms.
- Subjects
MATRICES (Mathematics); BOUNDARY value problems; GALERKIN methods; ALGEBRAIC equations; COLLOCATION methods
- Publication
Tbilisi Mathematical Journal, 2018, Vol 11, Issue 2, p17
- ISSN
1875-158X
- Publication type
Article
- DOI
10.32513/tbilisi/1529460019