Abdul-Majid Wazwaz
Saint Xavier University
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Publication
Featured researches published by Abdul-Majid Wazwaz.
TAEBC-2009 | 2009
Abdul-Majid Wazwaz
Partial Differential Equations.- Basic Concepts.- First-order Partial Differential Equations.- One Dimensional Heat Flow.- Higher Dimensional Heat Flow.- One Dimensional Wave Equation.- Higher Dimensional Wave Equation.- Laplaces Equation.- Nonlinear Partial Differential Equations.- Linear and Nonlinear Physical Models.- Numerical Applications and Pade Approximants.- Solitons and Compactons.- Solitray Waves Theory.- Solitary Waves Theory.- The Family of the KdV Equations.- KdV and mKdV Equations of Higher-orders.- Family of KdV-type Equations.- Boussinesq, Klein-Gordon and Liouville Equations.- Burgers, Fisher and Related Equations.- Families of Camassa-Holm and Schrodinger Equations.
Applied Mathematics and Computation | 1999
Abdul-Majid Wazwaz
In this paper we propose a powerful modification of Adomian decomposition method that will accelerate the rapid convergence of the series solution. The validity of the modified technique is verified through illustrative examples. In all cases of differential and integral equations, we obtained excellent performance from the modified algorithm. The modification could lead to a promising approach for many applications in applied sciences.
Applied Mathematics and Computation | 2000
Abdul-Majid Wazwaz
In this paper, a reliable technique for calculating Adomian polynomials for nonlinear operators will be developed. The new algorithm offers a promising approach for calculating Adomian polynomials for all forms of nonlinearity. The algorithm will be illustrated by studying suitable forms of nonlinearity. A nonlinear evolution model will be investigated.
Mathematical and Computer Modelling | 2004
Abdul-Majid Wazwaz
In this paper, we establish exact solutions for nonlinear wave equations. A sine-cosine method is used for obtaining traveling wave solutions for these models with minimal algebra. The method is applied to selected physical models to illustrate the usage of our main results.
Archive | 1997
Abdul-Majid Wazwaz
Classifications of Integral Equations Fredholm Integral Equations Volterra Integral Equations Fredholm Integro-Differential Equations Volterra Integro-Differential Equations Singular Integral Equations Nonlinear Fredholm Integral Equations Nonlinear Volterra Integral Equations Applications of Integral Equations
Applied Mathematics and Computation | 2004
Abdul-Majid Wazwaz
In this work we employ the tanh method for traveling wave solutions of nonlinear equations. The study is extended to equations that do not have tanh polynomial solutions. The efficiency of the method is demonstrated by applying it for a variety of selected equations.
Applied Mathematics and Computation | 2001
Abdul-Majid Wazwaz
In this paper, a reliable algorithm is employed to investigate the differential equations of Lane-Emden type. The algorithm rests mainly on the Adomian decomposition method with an alternate framework designed to overcome the difficulty of the singular point. The proposed framework is applied to a generalization of Lane-Emden equations so that it can be used in differential equations of the same type.
Applied Mathematics and Computation | 2002
Abdul-Majid Wazwaz
Singular initial value problems, linear and nonlinear, homogeneous and nonhomogeneous, are investigated by using Adomian decomposition method. The solutions are constructed in the form of a convergent series. A new general formula is established. The approach is illustrated with few examples.
Applied Mathematics and Computation | 2001
Abdul-Majid Wazwaz; Salah M. El-Sayed
In this paper we present an efficient modification of the Adomian decomposition method that will facilitate the calculations. We then conduct a comparative study between the new modification and the modified decomposition method. The study is conducted through illustrative examples. The new modification introduces a promising tool for many linear and nonlinear models.
Chaos Solitons & Fractals | 2002
Abdul-Majid Wazwaz
The genuinely nonlinear dispersive K(m,n) equation, ut+(um)x+(un)xxx=0, which exhibits compactons: solitons with compact support, is investigated. New solitary-wave solutions with compact support are developed. The specific cases, K(2,2) and K(3,3), are used to illustrate the pertinent features of the proposed scheme. An entirely new general formula for the solution of the K(m,n) equation is established, and the existing general formula is modified as well.