Control of error in the homotopy analysis of nonlinear Klein–Gordon initial value problems

2013 ◽  
Vol 219 (12) ◽  
pp. 6494-6509 ◽  
Author(s):  
Matthew Russo ◽  
Robert A. Van Gorder
Keyword(s):  
Initial Value Problems ◽  
Initial Value ◽  
Homotopy Analysis ◽  
Klein Gordon ◽  
Control Of Error

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.

Sign in / Sign up

Export Citation Format

Share Document