scholarly journals Some Comparison of Solutions by Different Numerical Techniques on Mathematical Biology Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Susmita Paul ◽  
Sankar Prasad Mondal ◽  
Paritosh Bhattacharya ◽  
Kripasindhu Chaudhuri
Keyword(s):  
Mathematical Biology ◽  
Decomposition Method ◽  
Numerical Technique ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Volterra Model ◽  
Numerical Techniques ◽  
Numerical Examples ◽  
Adomian Decomposition ◽  
Ordinary Differential Equation Systems

We try to compare the solutions by some numerical techniques when we apply the methods on some mathematical biology problems. The Runge-Kutta-Fehlberg (RKF) method is a promising method to give an approximate solution of nonlinear ordinary differential equation systems, such as a model for insect population, one-species Lotka-Volterra model. The technique is described and illustrated by numerical examples. We modify the population models by taking the Holling type III functional response and intraspecific competition term and hence we solve it by this numerical technique and show that RKF method gives good results. We try to compare this method with the Laplace Adomian Decomposition Method (LADM) and with the exact solutions.

scholarly journals Solving Some Oscillatory Problems using Adomian Decomposition Method and Haar Wavelet Method

2020 ◽  
Vol 12 (3) ◽  
pp. 289-302 ◽  
Author(s):  
I. Haq ◽  
I. Singh
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Haar Wavelet ◽  
Numerical Techniques ◽  
Wavelet Method ◽  
Numerical Examples ◽  
Haar Wavelet Method ◽  
Adomian Decomposition

In this research, we presented two classical numerical techniques to solve some oscillatory problems arised in various applications of sciences and engineering. Adomian decomposition method (ADM) and Haar wavelet method (HWM) are utilized for this purpose. Some numerical examples have been performed to illustrate the accuracy of the present methods.

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.

scholarly journals Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Randhir Singh ◽  
Gnaneshwar Nelakanti ◽  
Jitendra Kumar
Keyword(s):  
Approximate Solution ◽  
Error Analysis ◽  
Integral Equations ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Numerical Examples ◽  
Recursive Scheme ◽  
Urysohn Integral Equations ◽  
Adomian Decomposition

We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and error analysis of the ADM. Moreover, three numerical examples are included to demonstrate the accuracy and applicability of the method.

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.

Solutions of the modified Kawahara equation with time-and space-fractional derivatives

2016 ◽  
Vol 7 (1) ◽  
pp. 10 ◽  
Author(s):  
M. Safavi ◽  
A. A. Khajehnasiri
Keyword(s):  
Approximate Solution ◽  
Fractional Differential Equations ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Time And Space ◽  
Kawahara Equation ◽  
Numerical Examples ◽  
Adomian Decomposition ◽  
Fractional Differential

In this paper, we consider fractional differential equations (FDEs), specially modified Kawahara equation with time and space fractional derivatives, also we use Adomian decomposition method (ADM) to approximate the exact solutions of this equation. The ADM method converts the FKEs to an iterated formula that approximate solution is computable. The numerical examples illustrate efficiency and accuracy of the proposed method.

scholarly journals Adomian method for solving Emden-Fowler equation of higher order

2020 ◽  
pp. 231-240
Author(s):  
Nuha Mohammed Dabwan ◽  
Yahya Qaid Hasan
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Higher Order ◽  
Numerical Examples ◽  
Adomian Decomposition ◽  
Adomian Method ◽  
Fowler Equation

Adomian Decomposition Method (ADM) is presented in this article to solve Emden-Fowler equation of higher order. We tested this method with several numerical examples that showed the reliability of the method in the finding of good approximate solutions.

scholarly journals ADOMIAN DECOMPOSITION METHOD FOR SOLVING SIMPLE PENDULUM OSCILLATORY PROBLEMS

2020 ◽  
Vol 9 (7) ◽  
pp. 45-53
Keyword(s):  
Comparative Study ◽  
Numerical Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Haar Wavelet ◽  
Oscillatory Motion ◽  
Wavelet Method ◽  
Numerical Examples ◽  
Simple Pendulum ◽  
Adomian Decomposition

In this research, Adomian decomposition method (ADM) is presented to find the numerical solution of the equations arising in oscillatory motion of a simple pendulum. For comparative study Haar wavelet method (HWM) is utilized. Numerical examples illustrate the accuracy of the Adomian decomposition method.

Based on the Improved Homotopy Perturbation Method for Solving Nonlinear Equations

2013 ◽  
Vol 275-277 ◽  
pp. 836-840
Author(s):  
Xi Qin He ◽  
Hai Yang Li
Keyword(s):  
Integral Equation ◽  
Perturbation Method ◽  
Nonlinear Equations ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

According to Nonlinear Fredholm differential and integral equation，it is proposed that the improved homotopy perturbation method is used to solve in this paper, and apply the numerical examples to compare the advantages among homotopy perturbation method, Adomian decomposition method and improved homotopy perturbation method . The results show that improved homotopy perturbation method is more effective.

scholarly journals An accelerated solution for some classes of nonlinear partial differential equations

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
I. L. El-Kalla ◽  
E. M. Mohamed ◽  
H. A. A. El-Saka
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Series Solution ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Partial Differential ◽  
Adomian Polynomials ◽  
Numerical Examples ◽  
Adomian Decomposition

AbstractIn this paper, we apply an accelerated version of the Adomian decomposition method for solving a class of nonlinear partial differential equations. This version is a smart recursive technique in which no differentiation for computing the Adomian polynomials is needed. Convergence analysis of this version is discussed, and the error of the series solution is estimated. Some numerical examples were solved, and the numerical results illustrate the effectiveness of this version.

scholarly journals Approximation Algorithm for a System of Pantograph Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Sabir Widatalla ◽  
Mohammed Abdulai Koroma
Keyword(s):  
Approximate Solution ◽  
Approximation Algorithm ◽  
Laplace Transform ◽  
Numerical Algorithm ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Examples ◽  
Adomian Decomposition ◽  
High Degree ◽  
Very High

We show how to adapt an efficient numerical algorithm to obtain an approximate solution of a system of pantograph equations. This algorithm is based on a combination of Laplace transform and Adomian decomposition method. Numerical examples reveal that the method is quite accurate and efficient, it approximates the solution to a very high degree of accuracy after a few iterates.

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