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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
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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 ...
Invariants of third‐order ordinary differential equations y′′′=f(x,y,y′,y′′) via point transformations
(
John Wiley and Sons Ltd
, 2016 , Article)
A new systematic method to find the relative invariant differentiation operators is developed. We incorporate this new approach with Lie's infinitesimal method to study the general class y′′′ = f(x, y, y′, y′′) under general ...
New parametric solutions of some abel equations
(
University of Miskolc
, 2016 , Article)
New parametric solutions of some Abel equations of second kind are found. The scheme for construction of these solutions utilizes a combination of differential invariants of a symmetry of an associated second order ODE and ...
Stagnation point flow study with water based nanoparticles aggregation over a stretching sheet: numerical solution
(
American Scientific Publishers
, 2016 , Article)
Intention of the current study is to examined the two dimensional stagnation point flow of waterbased nanofluid towards a stretching sheet. To simplify the problem similarity transformations are smearing on basic boundary ...
Embodied water for urban economy: A three-scale input-output analysis for Beijing 2010
(
Elsevier
, 2015 , Article)
The scheme of a three-scale input-output analysis is presented in this study to investigate the water use profile of the urban economy in Beijing. Defined as total water including direct and indirect water, embodied water ...
Effect of Lorentz forces on forced-convection nanofluid flow over a stretched surface
(
Elsevier B.V.
, 2016 , Article)
Magnetic nanofluid hydrothermal analysis over a plate is studied that includes consideration of thermal radiation. The Runge-Kutta (RK4) method is utilized to get solution of ODEs which are obtained from similarity solution. ...