Lie Symmetries and Partial Differential Equations(PDEs)
Keywords:Lie symmetries, the group of transformations, the infinitesimals generator, partial differential equations, invariant.
There are many well-known techniques for obtaining exact solutions for differential equations, but many of them are simply special cases of a few powerful symmetry methods. Lie symmetry methods are techniques for finding exact solutions of a wide variety of differential equations. In this paper, we discuss the use of Lie symmetries on PDEs of order two in two independent variables and show how they can be used to transform the governing equation into another equation with one less independent variable. In addition, for our case study we consider the PDE(the bond-pricing equation) and solve the equation using Lie symmetry methods.