scholarly journals Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability

2007 ◽  
Vol 31 (6) ◽  
pp. 1092-1108 ◽  
Author(s):  
Youssef Z. Boutros ◽  
Mina B. Abd-el-Malek ◽  
Nagwa A. Badran ◽  
Hossam S. Hassan
Keyword(s):  
Viscous Flow ◽  
Lie Group ◽  
Group Method ◽  
Two Dimensional ◽  
Lie Group Method ◽  
Expanding Or Contracting Walls

scholarly journals Lie Group Method for Solving the Negative-Order Kadomtsev–Petviashvili Equation (nKP)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 224
Author(s):  
Ghaylen Laouini ◽  
Amr M. Amin ◽  
Mohamed Moustafa
Keyword(s):  
Lie Group ◽  
Traveling Wave ◽  
Invariant Solution ◽  
Traveling Wave Solutions ◽  
Group Method ◽  
Lie Group Method ◽  
Reduced Equations ◽  
Wave Solutions ◽  
Negative Order ◽  
Petviashvili Equation

A comprehensive study of the negative-order Kadomtsev–Petviashvili (nKP) partial differential equation by Lie group method has been presented. Initially the infinitesimal generators and symmetry reduction, which were obtained by applying the Lie group method on the negative-order Kadomtsev–Petviashvili equation, have been used for constructing the reduced equations. In particular, the traveling wave solutions for the negative-order KP equation have been derived from the reduced equations as an invariant solution. Finally, the extended improved (G′/G) method and the extended tanh method are described and applied in constructing new explicit expressions for the traveling wave solutions. Many new and more general exact solutions are obtained.

scholarly journals Some Remarks on the Solution of Linearisable Second-Order Ordinary Differential Equations via Point Transformations

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Winter Sinkala
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lie Group ◽  
Second Order ◽  
Point Transformation ◽  
Group Method ◽  
Lie Group Method ◽  
Generic Solution ◽  
Point Transformations

Transformations of differential equations to other equivalent equations play a central role in many routines for solving intricate equations. A class of differential equations that are particularly amenable to solution techniques based on such transformations is the class of linearisable second-order ordinary differential equations (ODEs). There are various characterisations of such ODEs. We exploit a particular characterisation and the expanded Lie group method to construct a generic solution for all linearisable second-order ODEs. The general solution of any given equation from this class is then easily obtainable from the generic solution through a point transformation constructed using only two suitably chosen symmetries of the equation. We illustrate the approach with three examples.

scholarly journals Solving Nonlinear Differential Algebraic Equations by an Implicit Lie-Group Method

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chein-Shan Liu
Keyword(s):  
Closed Form ◽  
Lie Group ◽  
Iterative Scheme ◽  
Differential Algebraic Equations ◽  
Group Method ◽  
Computational Results ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Lie Group Method

We derive an implicit Lie-group algorithm together with the Newton iterative scheme to solve nonlinear differential algebraic equations. Four numerical examples are given to evaluate the efficiency and accuracy of the new method when comparing the computational results with the closed-form solutions.

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