Solution of Higher Order Partial Differential Equation by using Homotopy Analysis Method

2017 ◽  
Vol V (VIII) ◽  
pp. 1230-1234
Author(s):  
Vimal P. Gohil
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Homotopy Analysis Method ◽  
Higher Order ◽  
Order Partial Differential Equation ◽  
Analysis Method ◽  
Partial Differential ◽  
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.

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