The optimal homotopy analysis method applied on nonlinear time‐fractional hyperbolic partial differential equation s

2020 ◽  
Author(s):  
Ghenaiet Bahia ◽  
Adel Ouannas ◽  
Iqbal M. Batiha ◽  
Zaid Odibat
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Hyperbolic Partial Differential Equation ◽  
Partial Differential ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis

The Use of Homotopy Analysis Method to Solve the Time-Dependent Nonlinear Eikonal Partial Differential Equation

2011 ◽  
Vol 66 (5) ◽  
pp. 259-271 ◽  
Author(s):  
Mehdi Dehghan ◽  
Rezvan Salehi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Research Work ◽  
Time Dependent ◽  
Test Problems ◽  
Analysis Method ◽  
Partial Differential ◽  
Homotopy Analysis

In this research work a time-dependent partial differential equation which has several important applications in science and engineering is investigated and a method is proposed to find its solution. In the current paper, the homotopy analysis method (HAM) is developed to solve the eikonal equation. The homotopy analysis method is one of the most effective methods to obtain series solution. HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of a series solution. Furthermore, this method does not require any discretization, linearization or small perturbation and therefore reduces the numerical computation a lot. Some test problems are given to demonstrate the validity and applicability of the presented technique.

scholarly journals Optimal homotopy analysis solution of fingero-imbibition phenomenon in homogeneous porous medium with magnetic fluid effect

10.29007/kq3n ◽  
2018 ◽  
Author(s):  
Dipakkumar Prajapati ◽  
Narendrasinh Desai
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Porous Medium ◽  
Magnetic Fluid ◽  
Nonlinear Partial Differential Equation ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Double Phase ◽  
Homotopy Analysis ◽  
Homogeneous Porous Medium

The present paper discusses the fingero-imbibition phenomenon in a double phase dis- placement process through homogeneous porous medium with the involvement of a layer of magnetic fluid in the injected phase. This phenomenon has much importance in petroleum technology. The nonlinear partial differential equation governing this phenomenon with appropriate boundary conditions is solved by an optimal homotopy analysis method. The convergence of the solution is decided by minimizing discrete squared residual.

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