scholarly journals Power Series Solution for Solving Nonlinear Burgers-Type Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
E. López-Sandoval ◽  
A. Mello ◽  
J. J. Godina-Nava ◽  
A. R. Samana
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Series Solution ◽  
Solution Method ◽  
Nonlinear Partial Differential Equations ◽  
Time Dependent ◽  
Power Series Solution ◽  
Partial Linear ◽  
Linear Differential ◽  
Burgers Type Equations

Power series solution method has been traditionally used to solve ordinary and partial linear differential equations. However, despite their usefulness the application of this method has been limited to this particular kind of equations. In this work we use the method of power series to solve nonlinear partial differential equations. The method is applied to solve three versions of nonlinear time-dependent Burgers-type differential equations in order to demonstrate its scope and applicability.

scholarly journals Approximate Solutions of Nonlinear Partial Differential Equations by Modifiedq-Homotopy Analysis Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Shaheed N. Huseen ◽  
Said R. Grace
Keyword(s):  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Approximate Solutions ◽  
Power Series Solution ◽  
Analysis Method ◽  
Exactly Solvable ◽  
Homotopy Analysis

A modifiedq-homotopy analysis method (mq-HAM) was proposed for solvingnth-order nonlinear differential equations. This method improves the convergence of the series solution in thenHAM which was proposed in (see Hassan and El-Tawil 2011, 2012). The proposed method provides an approximate solution by rewriting thenth-order nonlinear differential equation in the form ofnfirst-order differential equations. The solution of thesendifferential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.

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