Papers by fawzi Abdelwahid
Zenodo (CERN European Organization for Nuclear Research), Aug 22, 2022
In recent years, new formulas of the two-dimensional differential transform have been proven by u... more In recent years, new formulas of the two-dimensional differential transform have been proven by using the definition of the transform. In this work, we use a new approach based on the definition of the transform and the summation properties to prove the two-dimensional differential transform of the product of two functions, then we used this result to establish other useful formulas. This study shows that this procedure can be used to find formulas for many complicated terms. This enables us to apply the differential transform method on many types of partial differential equations. To demonstrate this approach, we applied the dimensional differential transform method on selected equations and compared our results with analytical solutions obtained by other methods
INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH
In recent years, new formulas of the two-dimensional differential transform have been proven by u... more In recent years, new formulas of the two-dimensional differential transform have been proven by using the definition of the transform. In this work, we use a new approach based on the definition of the transform and the summation properties to prove the two-dimensional differential transform of the product of two functions, then we used this result to establish other useful formulas. This study shows that this procedure can be used to find formulas for many complicated terms. This enables us to apply the differential transform method on many types of partial differential equations. To demonstrate this approach, we applied the dimensional differential transform method on selected equations and compared our results with analytical solutions obtained by other methods
Journal of Advances in Mathematics and Computer Science
In this work, we reviewed the two-dimensional differential transform, and introduced the differen... more In this work, we reviewed the two-dimensional differential transform, and introduced the differential transform method (DTM). As an application, we used this technique to find approximate and exact solutions of selected non-linear partial differential equations, with constant or variable coefficients and compared our results with the exact solutions. This shows that the introduced method is very effective, simple to apply to linear and nonlinear problems and it reduces the size of computational work comparing with other methods.
British Journal of Applied Science & Technology, 2016
Abdelwahid Fawzi Existence Theorems For 90o Vortex Vortex Scattering Master of Science Thesis Dublin City University, 1993
Abdelwahid Fawzi a Series Solution Approach to Monopole Scattering Phd Thesis Dublin City University, 1998
International Journal of Mathematics Computation, Apr 26, 2013
ABSTRACT The Ward method is used to construct initial data which correspond to two monopoles on t... more ABSTRACT The Ward method is used to construct initial data which correspond to two monopoles on top of each other pulled apart without any cost in potential energy. A gauge is found in which the data are real and analytic. The corresponding analytic solution near the origin is studied looking backwards and forwards in time. The solution considered breaks the combined symmetry of time inversion and 90° rotation.
Contemporary Analysis and Applied Mathematics, 2012
We review the Adomian decomposition method for the case of a nonlinear differential equation with... more We review the Adomian decomposition method for the case of a nonlinear differential equation with a general operator involving a special parameter λ, and examine the Taylor series expansion of a nonlinear term represented by an analytic function. For this type of operator, this study shows that Adomian’s approach is a special choice corresponding to λ=1. This study also defines the Adomian polynomials and explains Adomian’s choices. As a result of this study, we feature Abdelwahid’s algorithm for generating the Adomian polynomials for different types of nonlinear terms, which is eminently suitable for symbolic programming by exploiting the sifting property of the well-known Kronecker delta function. Furthermore this procedure can be used to calculate the Adomian polynomials for any nonlinear term as represented by an analytic function. Finally this study indicates that the case of λ≠1 presents an interesting new challenge for future research and studies including the case of λ=λ(x) ...
Open Journal of Applied Sciences, 2013
In this work, we studied the performance of modified techniques of Adomian method applied to non-... more In this work, we studied the performance of modified techniques of Adomian method applied to non-linear Volterra integral equations of the second kind. This study shows that the modified techniques are reliable, efficient and easy to use through recursive relations that involve simple integrals. Furthermore, we found that the right choice and the proper implementation of the modified techniques reduce the computational difficulties and increase the speed of convergent, comparing with the standard Adomian method.
Reports on Mathematical Physics, 2001
ABSTRACT The Ward method is used to construct initial data which correspond to two monopoles on t... more ABSTRACT The Ward method is used to construct initial data which correspond to two monopoles on top of each other pulled apart without any cost in potential energy. A gauge is found in which the data are real and analytic. The corresponding analytic solution near the origin is studied looking backwards and forwards in time. The solution considered breaks the combined symmetry of time inversion and 90° rotation.
Journal of Mathematical Physics, 1994
The scattering of magnetic flux tubes in superconductors is studied First, we introduce the Abeha... more The scattering of magnetic flux tubes in superconductors is studied First, we introduce the Abehan-Higgs model, which describes vortices in a superconductor, and the Euler-Lagrange equations which minimize the energy density given by this model Static vortex solutions satisfying these equations are reviewed. A technique proposed by on Manton [1] in which slowly changing solutions are approximated by a special family of time-independent solutions is described. Time-dependent solutions over small intervals are also studied Then the existence and the symmetries of the time-dependent solutions are studied. This analysis rules out all cases other than 0°, 90° or 180° scattenng of two vortices The proof of the Cauchy-Kowalewskyi theorem for a system of first order quasi-linear partial differential equations of (n+1) independent variables and m unknown functions is given. The Taylor expansion of the initial data near the origin is studied. The Cauchy Kowalewskyi theorem is applied to find the solutions of the time-dependent Euler-Lagrange equations near the origin. This study proves that our solution describes 90° scattenng Mathematica programs to calculate the senes solutions are also supplied.
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Papers by fawzi Abdelwahid