On exact solution of Laplace equation with Dirichlet and Neumann boundary conditions by the homotopy analysis method

2007 ◽  
Vol 365 (5-6) ◽  
pp. 412-415 ◽  
Author(s):  
Mustafa Inc
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Laplace Equation ◽  
Homotopy Analysis Method ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Analysis Method ◽  
Homotopy Analysis

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 Series Solutions of Delay Integral Equations via a Modified Approach of Homotopy Analysis Method

2021 ◽  
pp. 4006-4018
Author(s):  
Shaheed N. Huseen ◽  
Ali S. Tayih
Keyword(s):  
Exact Solution ◽  
Integral Equations ◽  
Homotopy Analysis Method ◽  
Series Solutions ◽  
Analysis Method ◽  
Special Values ◽  
Convergence Parameter ◽  
Linear Delay ◽  
Homotopy Analysis ◽  
Infinite Sums

In this paper, the series solutions of a non-linear delay integral equations are considered by a modified approach of homotopy analysis method (MAHAM). We split the function   into infinite sums. The outcomes of the illustrated examples are included to confirm the accuracy and efficiency of the MAHAM. The exact solution can be obtained using special values of the convergence parameter.

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.

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.

Influence of Wall Properties on the Peristaltic Flow of a Nanofluid in View of the Exact Solutions: Comparisons with Homotopy Analysis Method

2014 ◽  
Vol 69 (5-6) ◽  
pp. 199-206 ◽  
Author(s):  
Abdelhalim Ebaid ◽  
Salem H. Alatawi
Keyword(s):  
Heat Transfer ◽  
Exact Solution ◽  
Heat Transfer Coefficient ◽  
Exact Solutions ◽  
Transfer Coefficient ◽  
Homotopy Analysis Method ◽  
Peristaltic Flow ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
The Heat Transfer Coefficient

No doubt, the exact solution of any physical system is considered optimal when it is available. Such exact solution is of great importance not only in validating the accuracy of the approximate solution obtained for the same problem but also to derive the correct physical interpretation of the involved physical phenomena. In this paper, the system of linear and nonlinear partial differential equations describing the peristaltic flow of a nanofluid in a channel with compliant walls has been solved exactly. These exact solutions have been implemented to explore the exact effects of Prandtl number Pr, thermophoresis parameter NT, Brownian motion parameter NB, and Eckert number Ec on the temperature, the nanoparticle concentration profiles, and the heat transfer coefficient Z(x). In addition, the exact results have been compared with a very recent work via the homotopy analysis method for the same problem. Although these comparisons showed that the published approximate results coincide with the current exact analysis, a few remarkable differences have been detected for the behaviour of the heat transfer coefficient.

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