The Adomian Decomposition Method for Solving Nonlinear Partial Differential Equation Using Maple

This chapter is about the, Variational iteration method (VIM); Adomian decomposition method and its modification has been applied to solve nonlinear partial differential equation of imbibition phenomenon in oil recovery process. The important condition of counter-current imbibition phenomenon as v i = − v n , has been considered here main aim, here is to determine the saturation of injected fluid S i x t during oil recovery process which is a function of distance ξ and time θ , therefore saturation S i is chosen as a dependent variable while x and t are chosen as independent variable. The solution of the phenomenon has been found by VIM, ADM and Laplace Adomian decomposition method (LADM). The effectiveness of our method is illustrated by different numerical.

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Solusi Persamaan Transport dengan Menggunakan Metode Dekomposisi Adomian Laplace

Journal of Mathematics, Computations, and Statistics ◽

10.35580/jmathcos.v2i2.12580 ◽

2020 ◽

Vol 2 (2) ◽

pp. 173

Author(s):

Wahidah Sanusi ◽

Syafruddin Side ◽

Beby Fitriani

Keyword(s):

Differential Equation ◽

Laplace Transform ◽

Transport Equation ◽

Decomposition Method ◽

Adomian Decomposition Method ◽

Nonlinear Ordinary Differential Equation ◽

Inverse Laplace Transform ◽

Partial Differential ◽

Adomian Decomposition ◽

Calculation Results

Abstrak. Penelitian ini mengkaji terbentuknya persamaan Transport dan menerapkan metode Dekomposisi Adomian Laplace dalam menentukan solusi persamaan Transport. Persamaan transport merupakan salah satu bentuk dari persamaan diferensial parsial. Bentuk umum persamaan Transport yaitu: Metode Dekomposisi Adomian Laplace merupakan kombinasi antara dua metode yaitu metode dekomposisi adomian dan transformasi laplace. Penyelesaian persamaan Transport dengan metode Dekomposisi Adomian Laplace dilakukan dengan cara menggunakan tranformasi Laplace, mensubstitusi nilai awal, menyatakan solusi dalam bentuk deret tak hingga dan menggunakan invers transformasi laplace . Metode ini juga merupakan metode semi analitik untuk menyelesaikan persamaan diferensial nonlinier. Berdasarkan hasil perhitungan, metode dekomposisi Adomian Laplace dapat menghampiri penyelesaian persamaan diferensial biasa nonlinear.Kata Kunci: Metode Dekomposisi Adomian Laplace, Persamaan Diferensial Parsial, Persamaan Transport.This research discusses the solving of Transport equation applying Laplace Adomian Decomposition Method. Transport equation is one form of partial differential equations. General form of Transport equation is: Laplace Adomian Decomposition Method that combine between Laplace transform and Adomian Decomposition Method. The steps used to solve Transport equation are applying Laplace transform, initial value substitution, defining a solution as infinite series, then using the inverse Laplace transform. This method is a semi analytical method to solve for nonlinear ordinary differential equation. Based on the calculation results, the Laplace Adomian decomposition method can solve the solution of nonlinear ordinary differential equation.Keywords: Laplace Adomian Decomposition Method, Partial Differential Equation, Transport Equation.

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Laplace Decomposition Method to Study Solitary Wave Solutions of Coupled Nonlinear Partial Differential Equation

ISRN Computational Mathematics ◽

10.5402/2012/423469 ◽

2012 ◽

Vol 2012 ◽

pp. 1-5

Author(s):

Arun Kumar ◽

Ram Dayal Pankaj

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Decomposition Method ◽

Numerical Solutions ◽

Kdv Equation ◽

Nonlinear Partial Differential Equation ◽

Weak Nonlinearity ◽

Partial Differential ◽

New Approach ◽

Laplace Decomposition Method

Analytical and numerical solutions are obtained for coupled nonlinear partial differential equation by the well-known Laplace decomposition method. We combined Laplace transform and Adomain decomposition method and present a new approach for solving coupled Schrödinger-Korteweg-de Vries (Sch-KdV) equation. The method does not need linearization, weak nonlinearity assumptions, or perturbation theory. We compared the numerical solutions with corresponding analytical solutions.

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Penerapan Metode Dekomposisi Adomian Laplace Dalam Menentukan Solusi Persamaan Panas

Journal of Mathematics, Computations, and Statistics ◽

10.35580/jmathcos.v1i2.9243 ◽

2019 ◽

Vol 1 (2) ◽

pp. 206

Author(s):

Muhammad Abdy ◽

Syafruddin Side ◽

Reza Arisandi

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Heat Equation ◽

Laplace Transform ◽

Calculation Result ◽

Decomposition Method ◽

Nonlinear Differential Equations ◽

Adomian Decomposition Method ◽

Adomian Decomposition ◽

Laplace Decomposition Method

Abstrak. Artikel ini membahas tentang penerapan Metode Dekomposisi Adomian Laplace (LADM) dalam menentukan solusi persamaan panas. Metode Dekomposisi Adomian Laplace merupakan metode semi analitik untuk menyelesaikan persamaan diferensial nonlinier yang mengkombinasikan antara tranformasi Laplace dan metode dekomposisi Adomian. Berdasarkan hasil perhitungan, metode dekomposisi Adomian Laplace dapat menghampiri penyelesaian persamaan diferensial biasa nonlinear.Kata kunci: Metode Dekomposisi Adomian Laplace, Persamaan Diferensial Parsial, Persamaan PanasAbstract. This study discusses the application of Adomian Laplace Decomposition Method (ALDM) in determining the solution of heat equation. Adomian Laplace Decomposition Method is a semi analytical method to solve nonlinear differential equations that combine Laplace transform and Adomian decomposition method. Based on the calculation result, Adomian Laplace decomposition method can approach the settlement of ordinary nonlinear differential equations.Keywords: Adomian Laplace Decomposition Method, Partial Differential Equation, Heat Equation.

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