scholarly journals Exact Solutions of Homogeneous Partial Differential Equation by A New Adomian Decomposition Method

2011 ◽  
Vol 11 ◽  
pp. 440-446 ◽  
Author(s):  
Bingquan Zhang ◽  
Jun Lu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Partial Differential ◽  
Adomian Decomposition

scholarly journals Solusi Persamaan Transport dengan Menggunakan Metode Dekomposisi Adomian Laplace

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.

scholarly journals Penerapan Metode Dekomposisi Adomian Laplace Dalam Menentukan Solusi Persamaan Panas

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.

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

scholarly journals Sinc-Galerkin method for solving hyperbolic partial differential equations

2018 ◽  
Vol 8 (2) ◽  
pp. 250-258 ◽  
Author(s):  
Aydin Secer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Galerkin Method ◽  
Hyperbolic Equations ◽  
Approximate Solutions ◽  
Equation System ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Numerical Examples

In this work, we consider the hyperbolic equations to determine the approximate solutions via Sinc-Galerkin Method (SGM). Without any numerical integration, the partial differential equation transformed to an algebraic equation system. For the numerical calculations, Maple is used. Several numerical examples are investigated and the results determined from the method are compared with the exact solutions. The results are illustrated both in the table and graphically.

scholarly journals Approximate solution of nonlinear ordinary differential equation using ZZ decomposition method

2020 ◽  
Vol 4 (1) ◽  
pp. 448-455
Author(s):  
Mulugeta Andualem ◽  
◽  
Atinafu Asfaw ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Approximate Solution ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Initial Value ◽  
Transform Method ◽  
Adomian Decomposition

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

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