Optimum Path of a Flying Object with Exponentially Decaying Density Medium

2009 ◽  
Vol 64 (7-8) ◽  
pp. 431-438 ◽  
Author(s):  
Said Abbasbandy ◽  
Mehmet Pakdemirli ◽  
Elyas Shivanian
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Dimensionless Form ◽  
Optimum Path ◽  
Homotopy Analysis

AbstractIn this paper, a differential equation describing the optimum path of a flying object is derived. The density of the fluid is assumed to be exponentially decaying with altitude. The equation is cast in to a dimensionless form and the exact solution is given. This equation is then analyzed by homotopy analysis method (HAM). The results showed in the figures reveal that this method is very effective and convenient.

scholarly journals The Convergence Study of the Homotopy Analysis Method for Solving Nonlinear Volterra-Fredholm Integrodifferential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Behzad Ghanbari
Keyword(s):  
Exact Solution ◽  
Homotopy Analysis Method ◽  
Integrodifferential Equations ◽  
Sufficient Condition ◽  
Analysis Method ◽  
Analytic Treatment ◽  
Homotopy Analysis ◽  
Convergence Study ◽  
Technique Comparison

We aim to study the convergence of the homotopy analysis method (HAM in short) for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.

scholarly journals On the Application of Homotopy Analysis Method to Fractional Differential Equations

2021 ◽  
pp. 1-18
Author(s):  
Khalid Suliman Aboodh ◽  
Abu baker Ahmed
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Homotopy Analysis Method ◽  
Fractional Derivatives ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Convergence Control ◽  
Fractional Differential ◽  
Convergence Control Parameter

In this paper, an attempt has been made to obtain the solution of linear and nonlinear fractional differential equations by applying an analytic technique, namely the homotopy analysis method (HAM). The fractional derivatives are described by Caputo’s sense. By this method, the solution considered as the sum of an infinite series, which converges rapidly to exact solution with the help of the nonzero convergence control parameter ℏ. Some examples are given to show the efficiently and accurate of this method. The solutions obtained by this method has been compared with exact solution. Also our graphical represented of the solutions have been given by using MATLAB software.

scholarly journals On the Solutions of Fractional Cauchy Problem Featuring Conformable Derivative

2018 ◽  
Vol 22 ◽  
pp. 01045 ◽  
Author(s):  
Mehmet Yavuz ◽  
Necati Özdemir
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Exact Solutions ◽  
Detailed Analysis ◽  
Analytical Solutions ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Conformable Derivative ◽  
Homotopy Analysis ◽  
Fractional Cauchy Problem

In this study, we have obtained analytical solutions of fractional Cauchy problem by using q-Homotopy Analysis Method (q-HAM) featuring conformable derivative. We have considered different situations according to the homogeneity and linearity of the fractional Cauchy differential equation. A detailed analysis of the results obtained in the study has been reported. According to the results, we have found out that our obtained solutions approach very speedily to the exact solutions.

A New Semi-Analytical Solution of the Telegraph Equation with Integral Condition

2011 ◽  
Vol 66 (12) ◽  
pp. 760-768 ◽  
Author(s):  
S. Abbasbandy ◽  
H. Roohani Ghehsarehb
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Iterative Algorithm ◽  
Homotopy Analysis Method ◽  
Integral Condition ◽  
Telegraph Equation ◽  
Current Work ◽  
Analysis Method ◽  
Numerical Examples ◽  
Homotopy Analysis

In the current work, the telegraph equation in its general form and with an integral condition is investigated. Also the well-known homotopy analysis method (HAM) is applied and an interesting iterative algorithm is proposed for solving the problem in general form. Some numerical examples are given and compared with the exact solution to show the effectiveness of the proposed method.

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