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Adomian Decomposition Method for Solving Boussinesq Equations Using Maple
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作者 Ameera Aljuhani Dalal Maturi Hashim Alshehri 《Applied Mathematics》 2023年第2期121-129,共9页
This paper uses the Adomian Decomposition Method (ADM) to solve Boussinesq equations using Maple. The Boussinesq approximation for water waves is a weakly nonlinear and long-wave approximation in fluid dynamics. The a... This paper uses the Adomian Decomposition Method (ADM) to solve Boussinesq equations using Maple. The Boussinesq approximation for water waves is a weakly nonlinear and long-wave approximation in fluid dynamics. The approximation is named after Joseph Boussinesq, who developed it in response to John Scott Russell’s observation of a wave of translation (also known as solitary wave or soliton). Bossinesq’s article from 1872 introduced the equations that are now known as the Boussinesq equations. Numerical methods are commonly utilized to solve nonlinear equation systems. In this paper, we investigate a nonlinear singly perturbed advection-diffusion problem. Using the usual Adomian Decomposition Method, we formulate an approximate linear advection-diffusion problem and investigate several practical numerical approaches for solving it (ADM). The Adomian Decomposition Method (ADM) is a powerful tool for numerical simulations and approximation analytic solutions. The Adomian Decomposition Method (ADM) is used to solve nonlinear advection differential equations using Maple by illustrating numerous examples. The findings are presented in the form of tables and graphs for several examples. For various examples, the findings are presented in the form of tables and graphs. The difference between the precise and numerical solutions indicates the Maple program solution’s efficacy, as well as the ease and speed with which it was acquired. 展开更多
关键词 adomian decomposition method Boussinesq Equations Maple 18
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Adomian Decomposition Method for Solving Time Fractional Burgers Equation Using Maple
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作者 Fayza Alwehebi Aatef Hobiny Dalal Maturi 《Applied Mathematics》 2023年第5期324-335,共12页
In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The ob... In this paper, the Adomian decomposition method was used to solve the Time Fractional Burger equation using Mabel program. This method was applied to a number of examples of the Time Fractional Burger Equation. The obtained numerical results were presented in the form of tables and graphics. The difference between the exact solutions and the numerical solutions shows us the effectiveness of the solution using the Mabel program and that this method gave accurate results and was close to the exact solution, in addition to its ability to obtain the numerical solution quickly and efficiently using the Mabel program. 展开更多
关键词 adomian decomposition method Time Fractional Burgers Equation Maple 18
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Application of the Modified Adomian Decomposition Method on a Mathematical Model of COVID-19
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作者 Justina Mulenga Patrick Azere Phiri 《Journal of Applied Mathematics and Physics》 2023年第9期2597-2614,共18页
In this study, we constructed and analysed a mathematical model of COVID-19 in order to comprehend the transmission dynamics of the disease. The reproduction number (R<sub>C</sub>) was calculated via the n... In this study, we constructed and analysed a mathematical model of COVID-19 in order to comprehend the transmission dynamics of the disease. The reproduction number (R<sub>C</sub>) was calculated via the next generation matrix method. We also used the Lyaponuv method to show the global stability of both the disease free and endemic equilibrium points. The results showed that the disease-free equilibrium point is globally asymptotically stable if R<sub>C</sub> R<sub>C</sub> > 1. We further used the Adomian decomposition method and the modified Adomian decomposition method to obtain the solutions of the model. Numerical analysis of the model was done using Sagemath 9.0 software. 展开更多
关键词 COVID-19 stability Analysis Equilibrium Points adomian decomposition method Modified adomian decomposition method Numerical Analysis
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Solving Different Types of Differential Equations Using Modified and New Modified Adomian Decomposition Methods
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作者 Justina Mulenga Patrick Azere Phiri 《Journal of Applied Mathematics and Physics》 2023年第6期1656-1676,共21页
The Modified Adomian Decomposition Method (MADM) is presented. A number of problems are solved to show the efficiency of the method. Further, a new solution scheme for solving boundary value problems with Neumann cond... The Modified Adomian Decomposition Method (MADM) is presented. A number of problems are solved to show the efficiency of the method. Further, a new solution scheme for solving boundary value problems with Neumann conditions is proposed. The scheme is based on the modified Adomian decomposition method and the inverse linear operator theorem. Several differential equations with Neumann boundary conditions are solved to demonstrate the high accuracy and efficiency of the proposed scheme. 展开更多
关键词 Neumann Conditions Modified adomian decomposition method solution scheme New Modified adomian decomposition method Differential Equations
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On the Application of Adomian Decomposition Method to Special Equations in Physical Sciences
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作者 Aishah Alsulami Mariam Al-Mazmumy +1 位作者 Huda Bakodah Nawal Alzaid 《American Journal of Computational Mathematics》 2023年第3期387-397,共11页
The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study a... The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study are the singular equations that arise in many physical science applications. Thus, through the application of the ADM, a generalized recursive scheme was successfully derived and further utilized to obtain closed-form solutions for the models under consideration. The method is, indeed, fascinating as respective exact analytical solutions are accurately acquired with only a small number of iterations. 展开更多
关键词 Iterative scheme adomian decomposition method Initial-Value Problems singular Ordinary Differential Equations
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The Natural Transform Decomposition Method for Solving Fractional Klein-Gordon Equation
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作者 Mohamed Elbadri 《Applied Mathematics》 2023年第3期230-243,共14页
In this paper, a coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Kl... In this paper, a coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Klein-Gordan equation. The (NTDM), is introduced to derive the approximate solutions in series form for this equation. Solutions have been drawn for several values of the time power. To identify the strength of the method, three examples are presented. 展开更多
关键词 Natural Transform adomian decomposition method Fractional Klein-Gordon Equation
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Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems
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作者 Nawal Al-Zaid Kholoud Alzahrani +1 位作者 Huda Bakodah Mariam Al-Mazmumy 《International Journal of Modern Nonlinear Theory and Application》 2023年第3期81-98,共18页
The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and... The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables. 展开更多
关键词 Linear Third Order BVPs shooting method adomian decomposition method Two-Point Boundary Value Problem
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Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method 被引量:11
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作者 M.SHEIKHOLESLAMI D.D.GANJI +1 位作者 H.R.ASHORYNEJAD H.B.ROKNI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第1期25-36,共12页
In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method (ADM). The traditional Navier-Stokes eq... In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method (ADM). The traditional Navier-Stokes equation of fluid mechanics and Maxwell's electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different a, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann :number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated. 展开更多
关键词 MAGNETOHYDRODYNAMIC Jeffery-Hamel flow adomian decomposition method nonlinear ordinary differential equation NANOFLUID
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SOLUTION OF SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS BY ADOMIAN DECOMPOSITION METHOD 被引量:2
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作者 Duan Junsheng An Jianye Xu Mingyu2 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第1期7-12,共6页
The aim of this paper is to apply the relatively new Adomian decomposition method to solving the system of linear fractional, in the sense of Riemann-Liouville and Caputo respectively, differential equations. The solu... The aim of this paper is to apply the relatively new Adomian decomposition method to solving the system of linear fractional, in the sense of Riemann-Liouville and Caputo respectively, differential equations. The solutions are expressed in terms of Mittag-Leffier functions of matric argument. The Adomian decomposition method is straightforward, applicable for broader problems and avoids the difficulties in applying integral transforms. As the order is 1, the result here is simplified to that of first order differential equation. 展开更多
关键词 rfractional calculus adomian decomposition method Mittag-Lemer function.
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Adomian decomposition method and Padé approximants for solving the Blaszak-Marciniak lattice 被引量:1
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作者 杨沛 陈勇 李志斌 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第11期3953-3964,共12页
The Adomian decomposition method (ADM) and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and math... The Adomian decomposition method (ADM) and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and mathematics. In some cases, the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached. To overcome the drawback, the Pade approximants, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. By using the ADM-Pade technique, the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone. Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems. 展开更多
关键词 adomian decomposition method Pade approximants Blaszak-Marciniak lattice soliton solution
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A Unification of the Concepts of the Variational Iteration, Adomian Decomposition and Picard Iteration Methods;and a Local Variational Iteration Method 被引量:1
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作者 Xuechuan Wang Satya N.Atluri 《Computer Modeling in Engineering & Sciences》 SCIE EI 2016年第6期567-585,共19页
This paper compares the variational iteration method(VIM),the Adomian decomposition method(ADM)and the Picard iteration method(PIM)for solving a system of first o rder n onlinear o rdinary d ifferential e quations(ODE... This paper compares the variational iteration method(VIM),the Adomian decomposition method(ADM)and the Picard iteration method(PIM)for solving a system of first o rder n onlinear o rdinary d ifferential e quations(ODEs).A unification of the concepts underlying these three methods is attempted by considering a very general iterative algorithm for VIM.It is found that all the three methods can be regarded as special cases of using a very general matrix of Lagrange multipliers in the iterative algorithm of VIM.The global variational iteration method is briefly reviewed,and further recast into a Local VIM,which is much more convenient and capable of predicting long term complex dynamic responses of nonlinear systems even if they are chaotic. 展开更多
关键词 VARIATIONAL ITERATION method adomian decomposition method PICARD ITERATION method AsYMPTOTIC technique nonlinear DYNAMICAL system
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Analytical solution of fractionally damped beam by Adomian decomposition method 被引量:1
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作者 梁祖峰 唐晓艳 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第2期219-228,共10页
The analytical solution of a viscoelastic continuous beam whose damping characteristics are described in terms of a fractional derivative of arbitrary order was derived by means of the AdoInian decomposition method. T... The analytical solution of a viscoelastic continuous beam whose damping characteristics are described in terms of a fractional derivative of arbitrary order was derived by means of the AdoInian decomposition method. The solution contains arbitrary initial conditions and zero input. For specific analysis, the initial conditions were assumed homogeneous, and the input force was treated as a special process with a particular beam. Two simple cases, step and impulse function responses, were considered respectively. Subsequently, some figures were plotted to show the displacement of the beam under different sets of parameters including different orders of the fractional derivatives. 展开更多
关键词 viscoelastic beam fractional derivative adomian decomposition method vibration
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Solving <i>nth</i>-Order Integro-Differential Equations Using the Combined Laplace Transform-Adomian Decomposition Method 被引量:1
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作者 Waleed Al-Hayani 《Applied Mathematics》 2013年第6期882-886,共5页
In this paper, the Combined Laplace Transform-Adomian Decomposition Method is used to solve nth-order integro-differential equations. The results show that the method is very simple and effective.
关键词 Integro-Differential EQUATIONs LAPLACE Transform method adomian decomposition method
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On Discrete Adomian Decomposition Method with Chebyshev Abscissa for Nonlinear Integral Equations of Hammerstein Type 被引量:1
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作者 H. O. Bakodah Mohamed Abdalla Darwish 《Advances in Pure Mathematics》 2012年第5期310-313,共4页
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 inte... 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. 展开更多
关键词 DIsCRETE adomian decomposition method HAMMERsTEIN CHEBYsHEV
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The Modified Adomian Decomposition Method for Nonlinear Fractional Boundary Value Problems 被引量:1
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作者 WANG Jie 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第2期238-245,共8页
We use the modified Adomian decomposition method(ADM) for solving the nonlinear fractional boundary value problem {D α0+u(x)=f(x,u(x)) ,0〈x〈1,3〈α≤4u(0)=α0, u″(0)=α2u(1)=β0,u″(1)β2where Dα... We use the modified Adomian decomposition method(ADM) for solving the nonlinear fractional boundary value problem {D α0+u(x)=f(x,u(x)) ,0〈x〈1,3〈α≤4u(0)=α0, u″(0)=α2u(1)=β0,u″(1)β2where Dα 0 +u is Caputo fractional derivative and α0, α2, β0, β2 is not zero at all, and f : [0, 1] × R→R is continuous. The calculated numerical results show reliability and efficiency of the algorithm given. The numerical procedure is tested on lineax and nonlinear problems. 展开更多
关键词 Caputo fractional derivative adomian decomposition method differential equations
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On the Application of the Adomian’s Decomposition Method to a Generalized Thermoelastic Infinite Medium with a Spherical Cavity in the Framework Three Different Models 被引量:1
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作者 Najat A.Alghamdi Hamdy M.Youssef 《Fluid Dynamics & Materials Processing》 EI 2019年第5期597-611,共15页
A mathematical model is elaborated for a thermoelastic infinite body with a spherical cavity.A generalized set of governing equations is formulated in the context of three different models of thermoelasticity:the Biot... A mathematical model is elaborated for a thermoelastic infinite body with a spherical cavity.A generalized set of governing equations is formulated in the context of three different models of thermoelasticity:the Biot model,also known as“coupled thermoelasticity”model;the Lord-Shulman model,also referred to as“generalized thermoelasticity with one-relaxation time”approach;and the Green-Lindsay model,also called“generalized thermoelasticity with two-relaxation times”approach.The Adomian’s decomposition method is used to solve the related mathematical problem.The bounding plane of the cavity is subjected to harmonic thermal loading with zero heat flux and strain.Numerical results for the temperature,radial stress,strain,and displacement are represented graphically.It is shown that the angular thermal load and the relaxation times have significant effects on all the studied fields. 展开更多
关键词 adomians decomposition method generalized thermoelasticity relaxation time iteration method
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Nonlinear Problems via a Convergence Accelerated Decomposition Method of Adomian 被引量:1
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作者 Mustafa Turkyilmazoglu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第4期1-22,共22页
The present paper is devoted to the convergence control and accelerating the traditional Decomposition Methodof Adomian (ADM). By means of perturbing the initial or early terms of the Adomian iterates by adding aparam... The present paper is devoted to the convergence control and accelerating the traditional Decomposition Methodof Adomian (ADM). By means of perturbing the initial or early terms of the Adomian iterates by adding aparameterized term, containing an embedded parameter, new modified ADM is constructed. The optimal value ofthis parameter is later determined via squared residual minimizing the error. The failure of the classical ADM is alsoprevented by a suitable value of the embedded parameter, particularly beneficial for the Duan–Rach modification ofthe ADM incorporating all the boundaries into the formulation. With the presented squared residual error analysis,there is no need to check out the results against the numerical ones, as usually has to be done in the traditional ADMstudies to convince the readers that the results are indeed converged to the realistic solutions. Physical examplesselected from the recent application of ADM demonstrate the validity, accuracy and power of the presented novelapproach in this paper. Hence, the highly nonlinear equations arising from engineering applications can be safelytreated by the outlined method for which the classical ADM may fail or be slow to converge. 展开更多
关键词 Nonlinear equations adomian decomposition method MODIFICATION convergence acceleration
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Adomian Decomposition Method and Padé Approximants for Nonlinear Differential-Difference Equations 被引量:1
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作者 LIU Yan-Ming CHEN Yong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第4期581-587,共7页
Combining Adomian decomposition method (ADM) with Pade approximants, we solve two differentiaidifference equations (DDEs): the relativistic Toda lattice equation and the modified Volterra lattice equation. With t... Combining Adomian decomposition method (ADM) with Pade approximants, we solve two differentiaidifference equations (DDEs): the relativistic Toda lattice equation and the modified Volterra lattice equation. With the help of symbolic computation Maple, the results obtained by ADM-Pade technique are compared with those obtained by using ADM alone. The numerical results demonstrate that ADM-Pade technique give the approximate solution with faster convergence rate and higher accuracy and relative in larger domain of convergence than using ADM. 展开更多
关键词 adomian decomposition method Pade approximants relativistic Toda lattice equation modified Volterra lattice equation
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Solitary Wave Solutions of Discrete Complex Ginzburg-Landau Equation by Modified Adomian Decomposition Method 被引量:1
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作者 WANG Yue-Yue DAI Chao-Qing ZHANG Jie-Fang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第1期81-89,共9页
In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method (mADM), which is an efficient... In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method (mADM), which is an efficient method and does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions are also compared with their corresponding analytical solutions. It is shown that a very good approximation is achieved with the analytical solutions. Finally, the modulational instability is investigated and the corresponding condition is given. 展开更多
关键词 discrete complex Ginzburg-Landau equation modified adomian decomposition method solitary wave solutions modulational instability
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The Adomian Decomposition Method for a Type of Fractional Differential Equations 被引量:1
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作者 Peng Guo 《Journal of Applied Mathematics and Physics》 2019年第10期2459-2466,共8页
Fractional differential equations are widely used in many fields. In this paper, we discussed the fractional differential equation and the applications of Adomian decomposition method. Where the fractional operator is... Fractional differential equations are widely used in many fields. In this paper, we discussed the fractional differential equation and the applications of Adomian decomposition method. Where the fractional operator is in Caputo sense. Through the numerical test, we can find that the Adomian decomposition method is a powerful tool for solving linear and nonlinear fractional differential equations. The numerical results also show the efficiency of this method. 展开更多
关键词 Caputo FRACTIONAL INTEGRAL adomian decomposition method APPROXIMATE
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