The Quotient Homotopy Analysis Method for Solving Nonlinear Initial Value Problems

2021 ◽  
Author(s):  
Jamal Oudetallah ◽  
Ghenaiet Bahia ◽  
Adel Ouannas ◽  
Iqbal M. Batiha
Keyword(s):  
Homotopy Analysis Method ◽  
Initial Value Problems ◽  
Analysis Method ◽  
Initial Value ◽  
Homotopy Analysis

scholarly journals Solutions of the heat-conduction model described by fractional Emden-Fowler type equation

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 113-120 ◽  
Author(s):  
Chunfu Wei ◽  
Huanhuan Wang
Keyword(s):  
Heat Conduction ◽  
Homotopy Analysis Method ◽  
Initial Value Problems ◽  
Type Equation ◽  
Approximate Solutions ◽  
Time Dependent ◽  
Analysis Method ◽  
Initial Value ◽  
Conduction Model ◽  
Homotopy Analysis

In this paper, we presented a reliable algorithm to solve the singularity initial value problems of the time-dependent fractional Emden-Fowler type equations by homotopy analysis method. The approximate solutions of the problems are obtained.

scholarly journals A New Piecewise-Spectral Homotopy Analysis Method for Solving Chaotic Systems of Initial Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
H. Saberi Nik ◽  
Sohrab Effati ◽  
Sandile S. Motsa ◽  
Stanford Shateyi
Keyword(s):  
Homotopy Analysis Method ◽  
Initial Value Problems ◽  
System Modeling ◽  
Equation System ◽  
Analysis Method ◽  
Initial Value ◽  
Homotopy Analysis ◽  
Highly Oscillatory ◽  
First Time ◽  
Spectral Homotopy Analysis Method

An accurate algorithm for solving initial value problems (IVPs) which are highly oscillatory is proposed. The proposed method is based on a novel technique of extending the standard spectral homotopy analysis method (SHAM) and adapting it to a sequence of multiple intervals. In this new application the method is referred to as the piecewise spectral homotopy analysis method (PSHAM). The applicability of the proposed method is examined on the differential equation system modeling HIV infection of CD4+T cells and the Genesio-Tesi system which is known to be chaotic and highly oscillatory. Also, for the first time, we present here a convergence proof for SHAM. We treat in detail Legendre collocation and Chebyshev collocation. The method is compared to MATLAB’sode45inbuilt solver as a measure of accuracy and efficiency.

scholarly journals SOLUTIONS OF FRATIONAL EMDEN-FOWLER EQUATIONS BY HOMOTOPY ANALYSIS METHOD

2018 ◽  
Vol 13 (1) ◽  
pp. 7042-7047 ◽  
Author(s):  
Huan Huan Wang ◽  
Yue Hu
Keyword(s):  
Analytical Solution ◽  
Homotopy Analysis Method ◽  
Initial Value Problems ◽  
Approximate Analytical Solution ◽  
Analysis Method ◽  
Initial Value ◽  
Homotopy Analysis

In this paper, we have solved the singular initial value problems of fractional Emden-Fowler type equations by using the homotopy analysis method. The approximate analytical solution of this type equations are obtained.

scholarly journals Direct Solution ofnth-Order IVPs by Homotopy Analysis Method

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
A. Sami Bataineh ◽  
M. S. M. Noorani ◽  
I. Hashim
Keyword(s):  
Homotopy Analysis Method ◽  
Direct Solution ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Initial Value ◽  
Convergence Region ◽  
Runge Kutta Method ◽  
Approximate Analytical Solutions ◽  
Homotopy Analysis ◽  
Comparable Accuracy

Direct solution of a class ofnth-order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78).

On the piecewise-spectral homotopy analysis method and its convergence: solution of hyperchaotic Lü system

2014 ◽  
Vol 22 (4) ◽  
Author(s):  
S. S. Motsa ◽  
H. Saberi Nik ◽  
S. Effati ◽  
J. Saberi-Nadjafi
Keyword(s):  
Homotopy Analysis Method ◽  
Chaotic Behaviour ◽  
Model Systems ◽  
Analysis Method ◽  
Initial Value ◽  
Highly Nonlinear ◽  
Homotopy Analysis ◽  
Hyperchaotic Lu System ◽  
Spectral Homotopy Analysis Method ◽  
Good Agreement

Abstract- In this paper, a novel modification of the spectral-homotopy analysis method (SHAM) technique for solving highly nonlinear initial value problems that model systems with chaotic and hyper-chaotic behaviour is presented. The proposed method is based on implementing the SHAM on a sequence of multiple intervals thereby increasing it’s radius of convergence to yield highly accuratemethod which is referred to as the piece-wise spectral homotopy analysis method (PSHAM). We investigate the application of the PSHAM to the L¨u system [20] which is well known to display periodic, chaotic and hyper-chaotic behaviour under carefully selected values of it’s governing parameters. Existence and uniqueness of solution of SHAM that give a guarantee of convergence of SHAM, has been discussed in details. Comparisons are made between PSHAMgenerated results and results from literature and Runge-Kutta generated results and good agreement is observed.

Sign in / Sign up

Export Citation Format

Share Document