Application of Adomian decomposition method to nonlinear systems

Li, Wenjin; Pang, Yanni

doi:10.1186/s13662-020-2529-y

Cited by 55 publications

(34 citation statements)

References 45 publications

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“…Wenjin Li et al, [36] have presented the Adomian decomposition method (ADM for short)including its iterative scheme and convergence analysis, which was a simple andeffective technique in dealing with some nonlinear problems. Here, take algebraicequations and fractional differential equations as applications to illustrate ADM'sefficiency.…”

Section: Review Related On Adomian Decomposition Methodsmentioning

confidence: 99%

Existence of solutions for fixed point theorem

.Malathi¹,

Chelliah²

2021

JUSST

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The development of a mathematical model based on diffusion has received a great dealof attention in recent years, many scientist and mathematician have tried to apply basicknowledge about the differential equation and the boundary condition to explain anapproximate the diffusion and reaction model. The subject of fractional calculus attracted much attentions and is rapidly growing area of research because of itsnumerous applications in engineering and scientific disciplines such as signal processing, nonlinear control theory, viscoelasticity, optimization theory [1], controlled thermonuclear fusion, chemistry, nonlinear biological systems, mechanics,electric networks, fluid dynamics, diffusion, oscillation, relaxation, turbulence, stochastic dynamical system, plasmaphysics, polymer physics, chemical physics, astrophysics, and economics. Therefore, it deserves an independent theoryparallel to the theory of ordinary differential equations (DEs).In the development of non-linear analysis, fixed point theory plays an important role. Also, it has been widely used in different branches of engineering and sciences. Banach fixed point theory is a essential part of mathematical analysis because of its applications in various area such as variational and linear inequalities, improvement and approximation theory. The fixed-point theorem in diffusion equations plays a significant role to construct methods to solve the problems in sciences and mathematics. Although Banach fixed point theory is a vast field of study and is capable of solving diffusion equations. The main motive of the research is solving the diffusion equations by Banach fixed point theorems and Adomian decomposition method. To analysis the drawbacks of the other fixed-point theorems and different solving methods, the related works are reviewed in this paper.

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Section: Review Related On Adomian Decomposition Methodsmentioning

confidence: 99%

Existence of solutions for fixed point theorem

.Malathi¹,

Chelliah²

2021

JUSST

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“…The proposed method depends basically on applying some basic concepts in calculus [3,4] for the special case k = 0. In case k ̸ = 0, n ≥ 1, the Adomian decomposition method (ADM) [5][6][7][8][9][10][11][12][13][14] may be applied to solve the nonlinear system (1-2) which is a complex nonlinear initial value problem. The objectives of this paper are focused on estimating the falling time and comparing our results with the corresponding ones obtained from Newton's laws of vertical motion.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Accurate Time Calculations of Falling Bodies in the Earth's Gravitational Field and Comparisons with Newton's Laws of Vertical Motion

Ebaid

Al-Qahtani

Al-Jaber

et al. 2021

ARJOM

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The Earth is exposed annually to the fall of some meteorites and probably other celestial bodies which cause a potential danger to vital areas in several countries. Consequently, the accurate calculation of the falling time of such bodies is useful in order to take the necessary procedures for protecting these areas. In this paper, Newton’s law of general gravitation is applied to analyze the vertical motion in the Earth’s gravitational field. The falling time is obtained in exact form. The results are applied on several objects in real life.

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“…Metode ini dapat digunakan untuk menyelesaikan persamaan-persamaan diferensial, baik linear maupun nonlinear (Li & Pang, 2020). Metode ini dapat diterapkan meskipun data awal belum diketahui secara pasti (Lu & Zheng, 2021;Silva & De Bortoli, 2021).…”

Section: Pendahuluanunclassified

Keakuratan Metode Dekomposisi Adomian Untuk Masalah Nilai Awal Yang Penyelesaian Eksaknya Memuat Titik Singular

Lede

Mungkasi

2021

TEOREMA

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Salah satu cabang ilmu matematika adalah persamaan diferensial. Artikel ini meyelesaikan masalah nilai awal (persamaan diferensial biasa yang dilengkapi dengan suatu data nilai awal fungsi) dengan menggunakan metode dekomposisi Adomian. Tujuan penelitian ini adalah untuk mengamati sifat penyelesaian dekomposisi Adomian apabila penyelesaian eksaknya memuat titik singular. Artikel ini mengambil suatu kasus uji persamaan diferensial untuk menunjukkan kinerja metode dekomposisi Adomian. Metode penelitian yang diterapkan adalah metode penyelesaian persamaan matematis secara hampiran ke dalam deret fungsi dan pengamatan hasil simulasi komputer. Hasil dari simulasi kasus uji menunjukkan bahwa penyelesaian dekomposisi Adomian sangat akurat untuk titik-titik di sekitar data awal. Akan tetapi, penyelesaian dekomposisi Adomian kurang akurat untuk titik-titik di sekitar titik singular dan untuk titik-titik yang jauh dari titik awal. Keakuratan di sini diartikan dengan nilai error mutlak dari hampiran, yaitu bahwa hampiran disebut akurat apabila error mutlaknya kecil.Kata kunci: Masalah nilai awal, metode dekomposisi Adomian, persamaan diferensial biasa

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Application of Adomian decomposition method to nonlinear systems

Cited by 55 publications

References 45 publications

Existence of solutions for fixed point theorem

Existence of solutions for fixed point theorem

Accurate Time Calculations of Falling Bodies in the Earth's Gravitational Field and Comparisons with Newton's Laws of Vertical Motion

Keakuratan Metode Dekomposisi Adomian Untuk Masalah Nilai Awal Yang Penyelesaian Eksaknya Memuat Titik Singular

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