New Development of Adomian Decomposition Method for Solving Second Order Ordinary Differential Equations

Al-Mekhlfi, Sumayah Ghaleb Othma; Hasan, Yahya Qaid

doi:10.53555/eijms.v6i1.44

Cited by 4 publications

(8 citation statements)

References 10 publications

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“…where now x k and y k , k ≥ 1 are the coefficients of expansion (11). One important property of the Adomian polynomials which we will exploit to develop our algorithms is the fact that the Adomian polynomials F k , k ≥ 1 are affine with respect to x k and y k .…”

Section: Adomian Polynomials and The Differential Transform Methodsmentioning

confidence: 99%

“…One can find also applications in other fields such as chemistry and biology. Explicit systems of ordinary differential equations can be easily solved by several methods such as Runge-Kutta method [7,8], the residual power series method [9], Adomian decomposition method [10,11,12,13], the homotopy perturbation method [14], the differential transform method (DTM) [15,16]. A comprehensive review of the DTM is given in [17].…”

Section: Introductionmentioning

confidence: 99%

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A Novel Computational Approach for Solving Fully Implicit Singular Systems of Ordinary Differential Equations

Benhammouda

2023

Preprint

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This paper presents a novel computational approach to solve fully implicit singular nonlinear systems of ordinary differential equations. These systems have a two fold difficulty: being fully implicit and singular at the same time. Such systems cannot be solved in general by software packages such as Maple due to their fully implicit structure. Furthermore, numerical methods like Runge-Kutta cannot be applied. The proposed method here is based on the idea of applying the differential transform method (DTM) directly to these systems while exploiting an important property of Adomian polynomials. This new idea has led to a general and efficient algorithm that can be easily implemented using Maple, Mathematica or Matlab. We stress here that our technique does not require transforming the implicit system in hands to an explicit differential system. Also our technique equips the DTM with a powerful tool to solve other fully implicit differential systems. To illustrate the capability and efficiency of the proposed method, four numerical examples that are not solvable by software packages like Maple are given. Numerical results show that our method has successfully solved these examples by providing the exact solutions in a convergent power series form.

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Section: Adomian Polynomials and The Differential Transform Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Novel Computational Approach for Solving Fully Implicit Singular Systems of Ordinary Differential Equations

Benhammouda

2023

Preprint

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“…Where the components u n (x, t) of the solution u(x, t) will determine recurrently specific algorithums Adomian polynomials [1,9,4].…”

Section: Modified Adomian Decomposition Methodsmentioning

confidence: 99%

“…transfer, riemannian geometry, applied probability, mathematical physics, and biology [7,10]. Recently, a great deal of interest has been focused on the convergence studies of the series solution obtained using ADM for a wide variety of stochastic and deterministic problems [2,5,9]. A number of researchers used the ADM method to solve PDEs by ADM. ADM for first order PDEs with unprescribed data [8], some modifications of ADM for nonlinear PDEs [3] , modified decomposition method (MDM) with new inverse differential operators for solving singular nonlinear IVPs in first-and second-order PDEs arising in fluid mechanics [7] and et al The main objective of this paper is to introduce a new technique method for solving singular and non-singular PDEs of the first order.…”

mentioning

confidence: 99%

The New Adomian Technique for Solving Singular and Non-singular Partial Differential Equations of First Order

Raana,

Hasan2

2023

BUJ

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In this paper, the proposed modification to Adomian decomposition method (ADM) is introduced. In addition, a new modification to solve singular and nonsingular initial-value problems (IVPs) in first order partial differential equations (PDEs) is investigated. Then, a discussion of how ADM can be used to solve singular and nonsingular IVPs is produced. Finally, some example are given to demonstrate the applicability of the results of paper. Key words; Adomian decomposition method; Nonlinear first-order PDE; Singular and nonsingular first-order partial differential equations. 1 Introduction Singular nonlinear partial differential equations (PDEs) arise in various physical phe- nomena in applied sciences and engineering from such areas as fluid mechanics and heat-

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“…This modification enables the approach to determine the operator for other types of differential equations, such as those in spherical or cylindrical coordinate systems [16].…”

Section: Introductionmentioning

confidence: 99%

A study on various types of immobilization of enzyme kinetic mechanisms by comparing with the solutions obtained from AGM and MADM

Saravanakumar,

Veeramuni,

Veeramani

et al. 2024

Preprint

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In this article, the kinetic mechanisms are based on Michaelis-Menten reaction in presence of substrate inhibition have been solved by techniques ‘Akbari-Ganji’s Method’ (AGM) and ‘Modified Adomian decomposition method’ (MADM). Comparisons of solution of dimensionless substrate and product concentrations for various kinetic mechanisms have been carried out using AGM, MADM and numerical simulation. We assessed the impact of Thiele modulus, dimensionless inhibition degree, and concentration of substances outside the support on changing nature of substrate and product concentrations within the boundary layer in this study. The obtained results depict that the used methods have good accuracy for different values of kinetic parameters. Furthermore, the mean integrated effectiveness factor has been derived for all the mechanisms employing AGM solutions. This paper clearly illustrates the distinctions between MADM and AGM.

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New Development of Adomian Decomposition Method for Solving Second Order Ordinary Differential Equations

Cited by 4 publications

References 10 publications

A Novel Computational Approach for Solving Fully Implicit Singular Systems of Ordinary Differential Equations

A Novel Computational Approach for Solving Fully Implicit Singular Systems of Ordinary Differential Equations

The New Adomian Technique for Solving Singular and Non-singular Partial Differential Equations of First Order

A study on various types of immobilization of enzyme kinetic mechanisms by comparing with the solutions obtained from AGM and MADM

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