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Search Results: 1 - 10 of 4635 matches for " Huda Omar Bakodah "
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The Appearance of Noise Terms in Modified Adomian Decomposition Method for Quadratic Integral Equations  [PDF]
Huda Omar Bakodah
American Journal of Computational Mathematics (AJCM) , 2012, DOI: 10.4236/ajcm.2012.22017
Abstract: In this paper, we apply the modified Adomian Decomposition Method to get the numerical solutions of Quadratic integral equations. The appearance of noise terms in Decomposition Method was investigated. The method was described along with several examples.
A New Modification of the Method of Lines for First Order Hyperbolic PDEs  [PDF]
Fatmah M. Alabdali, Huda Omar Bakodah
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.510138

A new modification of the Method of Lines is proposed for the solution of first order partial differential equations. The accuracy of the method is shown with the matrix analysis. The method is applied to a number of test problems, on uniform grids, to compare the accuracy and computational efficiency with the standard method.

Numerical Treatment of Initial-Boundary Value Problems with Mixed Boundary Conditions  [PDF]
Nawal Abdullah Alzaid, Huda Omar Bakodah
American Journal of Computational Mathematics (AJCM) , 2018, DOI: 10.4236/ajcm.2018.82012
Abstract: In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.
Modified Adomain Decomposition Method for the Generalized Fifth Order KdV Equations  [PDF]
Huda O. Bakodah
American Journal of Computational Mathematics (AJCM) , 2013, DOI: 10.4236/ajcm.2013.31008

New modified Adomian decomposition method is proposed for the solution of the generalized fifth-order Korteweg-de Vries (GFKdV) equation. The numerical solutions are compared with the standard Adomian decomposition method and the exact solutions. The results are demonstrated which confirm the efficiency and applicability of the method.

A Comparative Study of Two Spatial Discretization Schemes for Advection Equation  [PDF]
Huda O. Bakodah
International Journal of Modern Nonlinear Theory and Application (IJMNTA) , 2016, DOI: 10.4236/ijmnta.2016.51006
Abstract: In this paper, we describe a comparison of two spatial discretization schemes for the advection equation, namely the first finite difference method and the method of lines. The stability of the methods has been studied by Von Neumann method and with the matrix analysis. The methods are applied to a number of test problems to compare the accuracy and computational efficiency. We show that both discretization techniques approximate correctly solution of advection equation and compare their accuracy and performance.
Numerical Solutions of the Regularized Long-Wave (RLW) Equation Using New Modification of Laplace-Decomposition Method  [PDF]
Nawal A. Al-Zaid, Huda O. Bakodah, Fathiah A. Hendi
Advances in Pure Mathematics (APM) , 2013, DOI: 10.4236/apm.2013.31A022

In this paper the new modification of Laplace Adomian decomposition method (ADM) to obtain numerical solution of the regularized long-wave (RLW) equation is presented. The performance of the method is illustrated by solving two test examples of the problem. To see the accuracy of the method, L2 and L error norms are calculated.

Soliton Solutions and Numerical Treatment of the Nonlinear Schrodinger’s Equation Using Modified Adomian Decomposition Method  [PDF]
Abeer Al-Shareef, Alyaa A. Al Qarni, Safa Al-Mohalbadi, Huda O. Bakodah
Journal of Applied Mathematics and Physics (JAMP) , 2016, DOI: 10.4236/jamp.2016.412215
Abstract: In this paper, the improved Adomian decomposition method (ADM) is applied to the nonlinear Schrödinger’s equation (NLSE), one of the most important partial differential equations in quantum mechanics that governs the propagation of solitons through optical fibers. The performance and the accuracy of our improved method are supported by investigating several numerical examples that include initial conditions. The obtained results are compared with the exact solutions. It is shown that the method does not need linearization, weak or perturbation theory to obtain the solutions.
On Discrete Adomian Decomposition Method with Chebyshev Abscissa for Nonlinear Integral Equations of Hammerstein Type  [PDF]
H. O. Bakodah, Mohamed Abdalla Darwish
Advances in Pure Mathematics (APM) , 2012, DOI: 10.4236/apm.2012.25042
Abstract: We study approximate solutions of a nonlinear integral equation of Hammerstein type. We describe the principle of discrete Adomian decomposition method (DADM). DADM is considered in the case we evaluate numerical integration by using Chebyshev roots. This technique gives an accurate solutions as will shown by illustrate examples.
Some modifications of Adomian decomposition method applied to nonlinear system of Fredholm integral equations of the second kind
H. O. Bakodah
International Journal of Contemporary Mathematical Sciences , 2012,
Recent Modifications of Adomian Decomposition Method for Initial Value Problem in Ordinary Differential Equations  [PDF]
M. Almazmumy, F. A. Hendi, H. O. Bakodah, H. Alzumi
American Journal of Computational Mathematics (AJCM) , 2012, DOI: 10.4236/ajcm.2012.23030
Abstract: In this paper, some modifications of Adomian decomposition method are presented for solving initial value problems in ordinary differential equations. Also, the restarted and two-step methods are applied to the problem. The effectiveness of the each modified is verified by several examples.
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