The Experts below are selected from a list of 3867 Experts worldwide ranked by ideXlab platform
Abdulmajid Wazwaz - One of the best experts on this subject based on the ideXlab platform.
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Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by the Adomian Decomposition Method
Journal of Mathematical Chemistry, 2014Co-Authors: Junsheng Duan, Randolph Rach, Abdulmajid WazwazAbstract:In this paper, we examine a system of two coupled nonlinear differential equations that relates the concentrations of carbon dioxide CO\(_2\) and phenyl glycidyl ether in solution. This system is subject to a set of Dirichlet boundary conditions and a mixed set of Neumann and Dirichlet boundary conditions. We apply the Adomian Decomposition Method combined with the Duan–Rach modified recursion scheme to analytically treat this system of coupled nonlinear boundary value problems. The rapid convergence of our analytic approximate solutions is demonstrated by graphs of the objective error analysis instead of comparison to an alternate solution technique alone. The Adomian Decomposition Method yields a rapidly convergent, easily computable, and readily verifiable sequence of analytic approximate solutions that is suitable for numerical parametric simulations. Thus our sequence of approximate solutions are shown to identically satisfy the original set of model equations as closely as we please.
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a study on the systems of the volterra integral forms of the lane emden equations by the Adomian Decomposition Method
Mathematical Methods in The Applied Sciences, 2014Co-Authors: Abdulmajid Wazwaz, Randolph Rach, Junsheng DuanAbstract:In this paper, we introduce systems of Volterra integral forms of the Lane–Emden equations. We use the systematic Adomian Decomposition Method to handle these systems of integral forms. The Volterra integral forms overcome the singular behavior at the origin x = 0. The Adomian Decomposition Method gives reliable algorithm for analytic approximate solutions of these systems. Our results are supported by investigating several numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.
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the combined laplace transform Adomian Decomposition Method for handling nonlinear volterra integro differential equations
Applied Mathematics and Computation, 2010Co-Authors: Abdulmajid WazwazAbstract:In this work, a combined form of the Laplace transform Method with the Adomian Decomposition Method is developed for analytic treatment of the nonlinear Volterra integro-differential equations. The combined Method is capable of handling both equations of the first and second kind. Illustrative examples will be examined to support the proposed analysis.
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a comparison between the variational iteration Method and Adomian Decomposition Method
Journal of Computational and Applied Mathematics, 2007Co-Authors: Abdulmajid WazwazAbstract:In this paper, we present a comparative study between the variational iteration Method and Adomian Decomposition Method. The study outlines the significant features of the two Methods. The analysis will be illustrated by investigating the homogeneous and the nonhomogeneous advection problems.
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Adomian Decomposition Method for a reliable treatment of the bratu type equations
Applied Mathematics and Computation, 2005Co-Authors: Abdulmajid WazwazAbstract:In this paper, we present a framework to determine exact solutions of Bratu-type equations. The algorithm rests mainly on the Adomian Decomposition Method. The proposed scheme is illustrated by studying two boundary value problems and an initial value problem of Bratu-type. The first type gives a solution that blows up at the middle of the domain, whereas the other equations give bounded solutions.
Junsheng Duan - One of the best experts on this subject based on the ideXlab platform.
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Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by the Adomian Decomposition Method
Journal of Mathematical Chemistry, 2014Co-Authors: Junsheng Duan, Randolph Rach, Abdulmajid WazwazAbstract:In this paper, we examine a system of two coupled nonlinear differential equations that relates the concentrations of carbon dioxide CO\(_2\) and phenyl glycidyl ether in solution. This system is subject to a set of Dirichlet boundary conditions and a mixed set of Neumann and Dirichlet boundary conditions. We apply the Adomian Decomposition Method combined with the Duan–Rach modified recursion scheme to analytically treat this system of coupled nonlinear boundary value problems. The rapid convergence of our analytic approximate solutions is demonstrated by graphs of the objective error analysis instead of comparison to an alternate solution technique alone. The Adomian Decomposition Method yields a rapidly convergent, easily computable, and readily verifiable sequence of analytic approximate solutions that is suitable for numerical parametric simulations. Thus our sequence of approximate solutions are shown to identically satisfy the original set of model equations as closely as we please.
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a study on the systems of the volterra integral forms of the lane emden equations by the Adomian Decomposition Method
Mathematical Methods in The Applied Sciences, 2014Co-Authors: Abdulmajid Wazwaz, Randolph Rach, Junsheng DuanAbstract:In this paper, we introduce systems of Volterra integral forms of the Lane–Emden equations. We use the systematic Adomian Decomposition Method to handle these systems of integral forms. The Volterra integral forms overcome the singular behavior at the origin x = 0. The Adomian Decomposition Method gives reliable algorithm for analytic approximate solutions of these systems. Our results are supported by investigating several numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.
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solving coupled lane emden boundary value problems in catalytic diffusion reactions by the Adomian Decomposition Method
Journal of Mathematical Chemistry, 2014Co-Authors: Randolph Rach, Junsheng DuanAbstract:In this paper, we consider the coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian Decomposition Method. First, we utilize systems of Volterra integral forms of the Lane–Emden equations and derive the modified recursion scheme for the components of the Decomposition series solutions. The numerical results display that the Adomian Decomposition Method gives reliable algorithm for analytic approximate solutions of these systems. The error analysis of the sequence of the analytic approximate solutions can be performed by using the error remainder functions and the maximal error remainder parameters, which demonstrate an approximate exponential rate of convergence.
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the Adomian Decomposition Method with convergence acceleration techniques for nonlinear fractional differential equations
Computers & Mathematics With Applications, 2013Co-Authors: Junsheng Duan, Temuer Chaolu, R RachAbstract:In this paper, we present the Adomian Decomposition Method and its modifications combined with convergence acceleration techniques, such as the diagonal Pade approximants and the iterated Shanks transforms, to solve nonlinear fractional ordinary differential equations. Two nonlinear numeric examples demonstrate that either the diagonal Pade approximants or the iterated Shanks transforms can efficiently extend the effective convergence region of the Decomposition series solution.
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Adomian Decomposition Method for solving the volterra integral form of the lane emden equations with initial values and boundary conditions
Applied Mathematics and Computation, 2013Co-Authors: Randolph Rach, Junsheng DuanAbstract:In this paper, we use the systematic Adomian Decomposition Method to handle the integral form of the Lane-Emden equations with initial values and boundary conditions. The Volterra integral form of the Lane-Emden equation overcomes the singular behavior at the origin x=0. We confirm our belief that the Adomian Decomposition Method provides efficient algorithm for analytic approximate solutions of the equation. Our results are supported by investigating several numerical examples that include initial value problems and boundary value problems as well. Finally we consider the modified Decomposition Method of Rach, Adomian and Meyers for the Volterra integral form.
Anjan Biswas - One of the best experts on this subject based on the ideXlab platform.
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bright optical solitons of chen lee liu equation with improved Adomian Decomposition Method
Optik, 2019Co-Authors: A S H F Mohammed, H. O. Bakodah, Anjan Biswas, M A Banaja, A A Alshaery, Qin Zhou, Seithuti P Moshokoa, Milivoj R BelicAbstract:Abstract This research work presents some numerical the results and analyses of three types of bright soliton solutions for the Chen-Lee-Liu (CLL) equation obtained from the improved Adomian Decomposition Method. The error analyses of the algorithm ae also discussed.
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optical soliton perturbation with kerr law nonlinearity by Adomian Decomposition Method
Optik, 2018Co-Authors: Anjan Biswas, Mir Asma, Rubayyi T AlqahtaniAbstract:Abstract This paper conducts numerical study of bright and dark optical solitons by the aid of Adomian Decomposition Method. The perturbed nonlinear Schrodinger's equation is studied where three perturbation terms of Hamiltonian type are included. The numerical scheme is first revisited and subsequently implemented to recover favorable simulations.
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w shaped optical solitons of chen lee liu equation by laplace Adomian Decomposition Method
Optical and Quantum Electronics, 2018Co-Authors: O Gonzalezgaxiola, Anjan BiswasAbstract:This paper studies Chen–Lee–Liu equation in optical fibers by the aid of Laplace Adomian Decomposition Method. The search is for W-shaped solitons numerically. The numerical results together with high level accuracy plots are exhibited.
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optical soliton perturbation with quadratic cubic nonlinearity by Adomian Decomposition Method
Optik, 2018Co-Authors: Mir Asma, Anjan Biswas, Wan Ainun Mior Othman, B R WongAbstract:Abstract This paper studies optical soliton perturbation that appears with quadratic-cubic nonlinearity, by the aid of Adomian Decomposition Method (ADM). Bright, dark and W-shaped solitons are examined that are obtained by the aid of this numerical scheme. The error plots are also given to give a taste of the accuracy of this scheme.
Liu Ming Zhu - One of the best experts on this subject based on the ideXlab platform.
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solving singular boundary value problems of higher order ordinary differential equations by modified Adomian Decomposition Method
Communications in Nonlinear Science and Numerical Simulation, 2009Co-Authors: Yahya Qaid Hasan, Liu Ming ZhuAbstract:Abstract In this paper, we use modified Adomian Decomposition Method to solving singular boundary value problems of higher-order ordinary differential equations. The proposed Method can be applied to linear and nonlinear problems. The scheme is tested for some examples and the obtained results demonstrate efficiency of the proposed Method.
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modified Adomian Decomposition Method for singular initial value problems in the second order ordinary differential equations
2008Co-Authors: Yahya Qaid Hasan, Liu Ming ZhuAbstract:In this paper an ecient modication of Adomian Decomposition Method is intro- duced for solving singular initial value problem in the second-order ordinary dierential equations. The scheme is tested for some examples and the obtained results demonstrate eciency of the proposed Method.
Jafar Biazar - One of the best experts on this subject based on the ideXlab platform.
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Extracting a general iterative Method from an Adomian Decomposition Method and comparing it to the variational iteration Method
Computers & Mathematics with Applications, 2010Co-Authors: Jafar Biazar, M. Gholami Porshokuhi, Behzad GhanbariAbstract:In this work, a new form of Adomian Decomposition Method (ADM) is presented; by this form a general iterative Method can be achieved in which there is no need of calculating Adomian polynomials. Also, this general iterative Method is compared with the Adomian Decomposition Method and variational iteration Method (VIM) and its advantages are expressed.
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solution of the epidemic model by Adomian Decomposition Method
Applied Mathematics and Computation, 2006Co-Authors: Jafar BiazarAbstract:In this article the problem of the spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic is considered. Mathematical modeling of the problem leads to a system of non-linear ordinary differential equations. Adomian Decomposition Method is employed to solve this system of non-linear ordinary differential equations, the problem of convergence has been addressed.
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solution of systems of integral differential equations by Adomian Decomposition Method
Applied Mathematics and Computation, 2005Co-Authors: Jafar BiazarAbstract:In this article Adomian Decomposition Method, as a well-known Method for solving functional equations, has been employed to solve systems of Integral-differential equations. Theoretical considerations are discussed, and convergence of the Method for these systems is addressed. Some examples are presented to show the ability of the Method for such systems.
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an approximation to the solution of hyperbolic equations by Adomian Decomposition Method and comparison with characteristics Method
Applied Mathematics and Computation, 2005Co-Authors: Jafar Biazar, H EbrahimiAbstract:Adomian Decomposition Method has been applied to solve many functional equations so far. In this work, this Method is applied to solve hyperbolic partial differential equations and results will be compared with characteristics Method.
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solution of a system of nonlinear equations by Adomian Decomposition Method
Applied Mathematics and Computation, 2004Co-Authors: Esmail Babolian, Jafar Biazar, A R VahidiAbstract:In this paper, the Adomian Decomposition Method is applied to solve a system of nonlinear equations. Convergence of the Method is proved and some examples are presented to illustrate the Method.