On 3rd order ordinary differential equations with maximal symmetry group

Computing ◽  
1996 ◽  
Vol 57 (3) ◽  
pp. 273-280 ◽  
Author(s):  
F. Schwarz
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Symmetry Group ◽  
Maximal Symmetry

Diverging type-D metrics

1977 ◽  
Vol 355 (1680) ◽  
pp. 31-52 ◽  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Symmetry Group ◽  
Two Dimensional ◽  
Field Equations ◽  
Killing Vectors ◽  
Type D

This paper contains an investigation of algebraically special spaces with two commuting Killing vectors. It is shown that the field equations for these spaces can be reduced to two ordinary differential equations, one of which is quasi-linear in one of the variables. The metric is type D iff it possesses a two dimensional, abelian, orthogonally transitive symmetry group. Finally, the type D metrics of Kinnersley are expressed in various coordinates, including those of Plebanski and Demianski.

Symmetries, integrals and solutions of ordinary differential equations of maximal symmetry

2010 ◽  
Vol 120 (1) ◽  
pp. 113-130 ◽  
Author(s):  
P. G. L. Leach ◽  
R. R. Warne ◽  
N. Caister ◽  
V. Naicker ◽  
N. Euler
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Maximal Symmetry

scholarly journals New Solutions of the Heat Equation and Application to Thin Plate Heat Conduction

2020 ◽  
Vol Volume 14 ◽  
Keyword(s):  
Heat Conduction ◽  
Differential Equations ◽  
Heat Equation ◽  
Ordinary Differential Equations ◽  
Symmetry Group ◽  
Thin Plate ◽  
Lie Symmetry ◽  
Second Order ◽  
Group Generator ◽  
Plate Heat

Using a Lie symmetry group generator and a generalised form of Euler’s formula for solving second order ordinary differential equations, we determine new symmetries for the heat equation, leading to new solutions. As an application, we test a formula resulting from this approach on thin plate heat conduction

scholarly journals Lie Symmetry Group for Unsteady Free Convection Boundary-Layer Flow over a Vertical Surface

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 175
Author(s):  
Mina B. Abd-el-Malek ◽  
Nagwa A. Badran ◽  
Amr M. Amin ◽  
Anood M. Hanafy
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Symmetry Group ◽  
Transformation Method ◽  
Vertical Surface ◽  
Lie Symmetry ◽  
Convection Boundary Layer ◽  
Group Transformation ◽  
Layer Flow ◽  
Lie Symmetry Group Transformation

The Lie symmetry group transformation method was used to investigate the partial differential equations that model the motion of a natural convective unsteady flow past to a non-isothermal vertical flat surface. The one-parameter Lie group transformation was applied twice consecutively to convert the motion governing equations into a system of ordinary differential equations. The obtained system of ordinary differential equations was solved numerically using the Lobatto IIIA formula (implicit Runge–Kutta method). The effect of the Prandtl number on the temperature and velocity profiles is illustrated graphically.

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