Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem

Table 1

Extensions of the principal Lie algebra.

Forms		Symmetries
𝑘	𝐺	𝑋1=𝜕𝑥.
e^𝑝𝜃	e^𝑞𝜃	𝑋2=𝑥𝜕𝑥+2𝑝−𝑞𝜕^𝜃,𝑝≠𝑞.
𝑝	e^𝑞𝜃	𝑋2=𝑥𝜕𝑥−2𝑞𝜃𝜕^𝜃.
(1+𝜆𝜃)	(1+𝜆𝜃)^𝑝	𝑋2=𝑥𝜕𝑥+2(1+𝜆𝜃)𝜆(𝑝−2)𝜕^𝜃,𝑝≠−6
		𝑋2=2𝜆𝑥^2𝜕𝑥+𝑥(1+𝜆𝜃)𝜕𝜃,
		𝑋3=2𝜆𝑥𝜕𝑥+(1+𝜆𝜃)𝜕𝜃,𝑝=−6