An efficient technique for finding the eigenvalues of fourth-order Sturm–Liouville problems

Syam, Muhammed I.; Siyyam, Hani I.

doi:10.1016/j.chaos.2007.01.105

Cited by 33 publications

(41 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are several more methods which have been applied to approximate the eigensolutions of the fourth order SLP (1) with general separated self-adjoint boundary conditions (2). These methods are shooting method [3], oscillation method [2], an efficient method based on the Adomian decomposition method (ADM) [4], and variational iteration methods [5]. In 2002, Chanane [6] applied Fliess series to compute the eigenvalues of the fourth-order Sturm-Liouville problems…”

Section: Introductionmentioning

confidence: 99%

Matrix methods for computing eigenvalues of Sturm–Liouville problems of order four

Rattana¹,

Böckmann²

2013

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

Bibliografische Information der Deutschen NationalbibliothekDie Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.de abrufbar. Universitätsverlag AbstractThis paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's method as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods are investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated.

show abstract

Section: Introductionmentioning

confidence: 99%

Matrix methods for computing eigenvalues of Sturm–Liouville problems of order four

Rattana¹,

Böckmann²

2013

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…Fractional derivatives have many applications, such as diffusion problems, liquid crystals, proteins, mechanics structural control, and biosystems [1][2][3][4][5][6][7][8][9]. Several analytical and numerical methods are used to solve fractional boundary and initial value problems, such as generalized differential transform, the Adomian decomposition method, the homotopy perturbation technique, fractional multistep methods, the spline approximation method, and the collocation method [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

An Implicit Hybrid Method for Solving Fractional Bagley-Torvik Boundary Value Problem

et al. 2018

View full text Add to dashboard Cite

show abstract

“…For instance, Lesnic and Attili [33] used the Adomian decomposition method (ADM) whereas Greenberg and Marletta [30]- [32] developed their own code using Theta Matrices (SLEUTH). Syam and Siyyam [34] implemented the iterated variation method. The present work is motivated by approximating the eigenvalues of problem (1.1)-(1.2) using reproducing kernel method (RKM).…”

Section: Introductionmentioning

confidence: 99%

A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems

Syam¹,

Al‐Mdallal²,

Al-Refai³

2017

Communications in Numerical Analysis

Self Cite

View full text Add to dashboard Cite

This article is devoted to both theoretical and numerical studies of eigenvalues of regular fractional 2α-order SturmLiouville problem where 1 2 < α ≤ 1. In this paper, we implement the reproducing kernel method RKM) to approximate the eigenvalues. To find the eigenvalues, we force the approximate solution produced by the RKM satisfy the boundary condition at x = 1. The fractional derivative is described in the Caputo sense. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the eigenfunctions of the proposed problem. Uniformly convergence of the approximate eigenfunctions produced by the RKM to the exact eigenfunctions is proven.

show abstract

An efficient technique for finding the eigenvalues of fourth-order Sturm–Liouville problems

Cited by 33 publications

References 18 publications

Matrix methods for computing eigenvalues of Sturm–Liouville problems of order four

Matrix methods for computing eigenvalues of Sturm–Liouville problems of order four

An Implicit Hybrid Method for Solving Fractional Bagley-Torvik Boundary Value Problem

A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems

Contact Info

Product

Resources

About