scholarly journals Homotopy Analysis Method for Solving Initial Value Problems of Second Order with Discontinuities

2019 ◽  
Vol 10 (06) ◽  
pp. 419-434
Author(s):  
Waleed Al-Hayani ◽  
Rasha Fahad
Keyword(s):  
Homotopy Analysis Method ◽  
Initial Value Problems ◽  
Second Order ◽  
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 Homotopy Analysis Method for Second-Order Boundary Value Problems of Integrodifferential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Ahmad El-Ajou ◽  
Omar Abu Arqub ◽  
Shaher Momani
Keyword(s):  
Homotopy Analysis Method ◽  
Series Solution ◽  
Convergent Series ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Analysis Method ◽  
Convergence Region ◽  
New Approach ◽  
Homotopy Analysis ◽  
And Control

In this paper, series solution of second-order integrodifferential equations with boundary conditions of the Fredholm and Volterra types by means of the homotopy analysis method is considered. The new approach provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. The homotopy analysis method provides us with a simple way to adjust and control the convergence region of the infinite series solution by introducing an auxiliary parameter. The proposed technique is applied to a few test examples to illustrate the accuracy, efficiency, and applicability of the method. The results reveal that the method is very effective, straightforward, and simple.

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