Symmetry and Integration Methods for Differential Equations

By George Bluman, Stephen C. Anco. 2002

1,101 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/e0f0f59e679093f847b6e1857ac3c36e2a7f56a5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

A Survey on the Inverse Integrating Factor (2009, methodology): “Based on these ideas, Bluman and Anco [6] argue heuristically that separatrices should also lie in V −1(0).”
Lessons Learned from Quantitative Dynamical Modeling in Systems Biology (2013, background): “The corresponding reparameterization does not restrict the dynamics of the model and is also known as nondimensionalization [24].”
Lie Group Solution for Free Convective Flow of a Nanofluid Past a Chemically Reacting Horizontal Plate in a Porous Media (2014, methodology): “Lie group analysis has been used by many investigators to analyze various convective phenomena under various flow configurations arising in fluidmechanics, aerodynamics, plasma physics, meteorology, chemical engineering, and other engineering branches [29].”
On the group classification of variable-coefficient nonlinear diffusion-convection equations (2006, methodology): “This method is easy to apply and well established in the last few years [3,5,11,16,28,39].”
On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations (2004, positive): “…to identify such integrable dynamical systems different techniques have been proposed, including Painlevé analysis (Conte 1999), Lie symmetry analysis Article submitted to Royal Society TEX Paper (Bluman & Anco 2002) and direct methods of finding involutive integrals of motion (Hietarinta 1987).”
Invariant analysis of time fractional generalized Burgers and Korteweg–de Vries equations (2012, background): “It is well known that the Lie group of transformations theory, originally advocated by the Norwegian mathematician Sophus Lie in the beginning of the 19th century, plays a significant role in the analysis of differential equations [1–6].”
Exterior Differential Systems with Symmetry (2005, neutral): “The fourth order diﬀerential equation on pg. 156 (Bluman and Anco, 2002) x deﬁnes the completely integrable Pfaﬃan system and action on is a symmetry group of I which acts freely on M . on The Lie algebra of inﬁnitesimal generators M is Let U = { ( t, y ) ∈ IR 2 | y = 2 t 2 − t be coordinates on…”
A group invariant solution for a pre-existing fluid-driven fracture in permeable rock (2011, background): “The theory of Lie groupanalysis of differential equations which has extensively been dealt with in several books[18, 19, 20, 21, 22] was initiated by the19th century Norwegian mathematician, Sophus Lie (1842-1899).”
Symmetry group classification of ordinary differential equations: Survey of some results (2007, background): “Bluman GW, Anco S. Symmetry and Integration Methods for Differential Equations.”