Harmonic numbers operational matrix for solving fifthorder two point boundary value problems
Y.H. Youssri$^{1}$ and W.M. AbdElhameed$^{2}$
The principal purpose of this paper is to present and implement two numerical algorithms for solving
linear and nonlinear fifthorder 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 wellknown harmonic numbers. The key idea
for the two proposed numerical algorithms is based on converting the linear or nonlinear fifthorder two
BVPs into systems of linear or nonlinear algebraic equations by employing PetrovGalerkin or collocation
spectral methods. Numerical tests are presented aiming to ascertain the high efficiency and accuracy of
the two proposed algorithms.
Tbilisi Mathematical Journal, Vol. 11(2) (2018), pp. 1733
