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On computing joint invariants of vector fields
(
Elsevier
, 2015 , Article)
A constructive version of the Frobenius integrability theorem-that can be programmed effectively-is given. This is used in computing invariants of groups of low ranks and recover examples from a recent paper of Boyko etal. (2009).
A point symmetry based method for transforming ODEs with three-dimensional symmetry algebras to their canonical forms
(
Elsevier Inc.
, 2016 , Article)
We provide an algorithmic approach to the construction of point transformations for scalar ordinary differential equations that admit three-dimensional symmetry algebras which lead to their respective canonical forms.
Approximate analytic solutions of transient nonlinear heat conduction with temperature-dependent thermal diffusivity
(
Hindawi Publishing Corporation
, 2014 , Article)
A new approach for generating approximate analytic solutions of transient nonlinear heat conduction problems is presented. It is based on an effective combination of Lie symmetry method, homotopy perturbation method, finite ...
Embedding algorithms and applications to differential equations
(
Academic Press
, 2018 , Article)
Algorithms for embedding certain types of nilpotent subalgebras in maximal subalgebras of the same type are developed, using methods of real algebraic groups. These algorithms are applied to determine non-conjugate subalgebras ...
Theoretical analysis of upper-convected Maxwell fluid flow with Cattaneo-Christov heat flux model
(
Physical Society of the Republic of China
, 2017 , Article)
This paper discusses the mixed convection three-dimensional boundary layer flow of upper-convected Maxwell fluid over a stretching surface with Cattaneo-Christov heat flux model. Magnetohydrodynamic (MHD) combined with ...
Linearization of third-order ordinary differential equations u'''=f(x,u,u',u') via point transformations
(
John Wiley and Sons Ltd
, 2018 , Article)
The linearization problem for scalar third-order ordinary differential equations via point transformations was solved partially in the works of Al-Dweik et al by the use of the Cartan equivalence method. In order to solve ...
Analysis of ferrite nanoparticles in the flow of ferromagnetic nanofluid
(
Public Library of Science
, 2018 , Article)
Theoretical analysis has been carried out to establish the heat transport phenomenon of six different ferromagnetic MnZnFe2O4-C2H6O2 (manganese zinc ferrite-ethylene glycol), NiZnFe2O4-C2H6O2 (Nickel zinc ferrite-ethylene ...
Quantization of the Szekeres system
(
Institute of Physics Publishing
, 2018 , Article)
We study the quantum corrections on the Szekeres system in the context of canonical quantization in the presence of symmetries. We start from an effective point-like Lagrangian with two integrals of motion, one corresponding ...
Invariant solutions of the Wave equation on static spherically symmetric spacetimes admitting G7 isometry algebra
(
MDPIAG
, 2018 , Article)
Algorithms to construct the optimal systems of dimension of at most three of Lie algebras are given. These algorithms are applied to determine the Lie algebra structure and optimal systems of the symmetries of the wave ...
Invariant characterization of scalar third-order ODEs that admit the maximal point symmetry Lie algebra
(
John Wiley and Sons Ltd
, 2018 , Article)
The Cartan equivalence method is used to deduce an invariant characterization of the scalar third-order ordinary differential equation u"' = f(x, u, u', u"), which admits the maximal 7-dimensional point symmetry Lie algebra. ...