Shaher Momani

Bio: Shaher Momani is an academic researcher from University of Jordan. The author has contributed to research in topics: Fractional calculus & Nonlinear system. The author has an hindex of 64, co-authored 301 publications receiving 13680 citations. Previous affiliations of Shaher Momani include Aberystwyth University & Al-Balqa` Applied University.

Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order

Abstract: In this paper, the variational iteration method is implemented to give approximate solutions for nonlinear differential equations of fractional order. In this method the problems are initially approximated by imposing the initial conditions. Then a correction functional for the fractional differential equation is well constructed by a general Lagrange multiplier, which can be identified optimally via variational theory. The iteration method, which produces the solutions in terms of convergent series with easily computable components, requiring no linearization or small perturbation. Some examples are given and comparisons are made with the Adomian decomposition method. The comparison shows that the method is very effective and convenient and overcome the difficulty arising in calculating Adomian polynomials.

Application of He’s variational iteration method to Helmholtz equation

Abstract: In this article, we implement a new analytical technique, He’s variational iteration method for solving the linear Helmholtz partial differential equation. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers in the functionals can be identified optimally via the variational theory. The initial approximations can be freely chosen with possible unknown constants, which can be determined by imposing the boundary/initial conditions. The results compare well with those obtained by the Adomian’s decomposition method.

Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order

Abstract: In this paper, a modification of He’s homotopy perturbation method is presented. The new modification extends the application of the method to solve nonlinear differential equations of fractional order. In this method, which does not require a small parameter in an equation, a homotopy with an imbedding parameter p ∈ [0, 1] is constructed. The proposed algorithm is applied to the quadratic Riccati differential equation of fractional order. The results reveal that the method is very effective and convenient for solving nonlinear differential equations of fractional order.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Some asymptotic methods for strongly nonlinear equations

Abstract: This paper features a survey of some recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the obtained approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modied perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to overcome the shortcomings. In this paper the following categories of asymptotic methods are emphasized: (1) variational approaches, (2) parameter-expanding methods, (3) parameterized perturbation method, (4) homotopy perturbation method (5) iteration perturbation method, and ancient Chinese methods. The emphasis of this article is put mainly on the developments in this eld in China so the references, therefore, are not exhaustive.