scholarly journals Analytical Solution for the Time-Dependent Emden-Fowler Type of Equations by Homotopy Analysis Method with Genetic Algorithm

2017 ◽  
Vol 08 (05) ◽  
pp. 693-711
Author(s):  
Waleed Al-Hayani ◽  
Laheeb Alzubaidy ◽  
Ahmed Entesar
Keyword(s):  
Genetic Algorithm ◽  
Analytical Solution ◽  
Homotopy Analysis Method ◽  
Time Dependent ◽  
Analysis Method ◽  
Homotopy Analysis

scholarly journals Analytical solution of Velocities and Temperature fields using Homotopy Analysis Method

2021 ◽  
Vol 12 (1S) ◽  
pp. 691-700
Author(s):  
Dr. K.V.Tamil Selvi , Et. al.
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Temperature Fields ◽  
Analysis Method ◽  
Partial Differential ◽  
Convective Boundary ◽  
Homotopy Analysis

In this paper, analysis of nonlinear partial differential equations on velocities and temperature with convective boundary conditions are investigated. The governing partial differential equations are transformed into ordinary differential equations by applying similarity transformations. The system of nonlinear differential equations are solved using Homotopy Analysis Method (HAM). An analytical solution is obtained for the values of Magnetic parameter M2, Prandtl number Pr, Porosity parameter

scholarly journals An Integrated Genetic Algorithm and Homotopy Analysis Method to Solve Nonlinear Equation Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hala A. Omar
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equation ◽  
Homotopy Analysis Method ◽  
Optimal Solution ◽  
Initial Guess ◽  
Analysis Method ◽  
Optimization Task ◽  
Homotopy Analysis ◽  
Newton Homotopy ◽  
Nonlinear Equation Systems

Solving nonlinear equation systems for engineering applications is one of the broadest and most essential numerical studies. Several methods and combinations were developed to solve such problems by either finding their roots mathematically or formalizing such problems as an optimization task to obtain the optimal solution using a predetermined objective function. This paper proposes a new algorithm for solving square and nonsquare nonlinear systems combining the genetic algorithm (GA) and the homotopy analysis method (HAM). First, the GA is applied to find out the solution. If it is realized, the algorithm is terminated at this stage as the target solution is determined. Otherwise, the HAM is initiated based on the GA stage’s computed initial guess and linear operator. Moreover, the GA is utilized to calculate the optimum value of the convergence control parameter (h) algebraically without plotting the h-curves or identifying the valid region. Four test functions are examined in this paper to verify the proposed algorithm’s accuracy and efficiency. The results are compared to the Newton HAM (NHAM) and Newton homotopy differential equation (NHDE). The results corroborated the superiority of the proposed algorithm in solving nonlinear equation systems efficiently.

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.

scholarly journals Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Hadi Hosseini Fadravi ◽  
Hassan Saberi Nik ◽  
Reza Buzhabadi
Keyword(s):  
Analytical Solution ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Convergent Series ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Foam Drainage Equation ◽  
Foam Drainage

The analytical solution of the foam drainage equation with time- and space-fractional derivatives was derived by means of the homotopy analysis method (HAM). The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made; the comparisons show that the homotopy analysis method is very effective and convenient. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained.

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