scholarly journals Lie group and RK4 for solving nonlinear first order ODEs

2016 ◽  
Vol 5 (2) ◽  
pp. 117
Author(s):  
Sami H. Altoum
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Numerical Method ◽  
Lie Group ◽  
Analytical Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Group Method ◽  
Numerical Comparison ◽  
First Order ◽  
Lie Group Method

This paper deals with a numerical comparison between Lie group method and RK4 for solving an nonlinear ordinary differential equation. The Lie group method will be introduced as a analytical method and then compared to RK4 as a numerical method. Some examples will be considered and the global error we be computed numerically.

Generalized Polar Decompositions in Matrix Exponential

2011 ◽  
Vol 130-134 ◽  
pp. 3023-3026
Author(s):  
Yi Min Tian ◽  
Ao Zhang
Keyword(s):  
Differential Equation ◽  
Lie Group ◽  
Analytic Solution ◽  
Matrix Exponential ◽  
Group Method ◽  
Lie Group Method ◽  
The Matrix ◽  
Numeric Solution ◽  
Basic Ideas ◽  
Solution Manifold

Matrix exponential computstion is a difficulty thing when the order of the matrix get big and big after discretion. When we use Lie group method to get numeric solution of a differential equation, we often face this problem.Li group method is a kind of prosperous method, its basic ideas is to keep the numeric solution in a manifold which is less than the Euclid space while bigger than the analytic solution manifold, so we can get more exact numeric solution than other method. So we discussed the generalized polar decompositions method for matrix exponential.

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.

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