We prove that any potential symmetry of a system of evolution equations reduces to a Lie symmetry through a nonlocal transformation of variables. Based on this fact is our method of group classification of potential symmetries of systems of evolution equations having non-trivial Lie symmetry. Next, we modify the above method to generate more general nonlocal symmetries, which yields a purely al...

Lie point symmetry analysis is performed for an unsteady nonlinear heat diffusion problem modeling thermal energy storage in a medium with a temperature-dependent power law thermal conductivity and subjected to a convective heat transfer to the surrounding environment at the boundary through a variable heat transfer coefficient. Large symmetry groups are admitted even for special choices of the...

Lie-symmetry based integrators are constructed in order to preserve the local invariance properties of the equations. The geometrical methods leading to discretized equations for numerical computations involve many different concepts. Therefore they give rise to numerical schemes that vary in the accuracy, in the computational cost and in the implementation. In this paper a comparison is made b...

Differential-difference equations (DDEs) of the form u n (t) = Fn(t, un+a, . . . , un+b) with k ≥ 2 are studied for Lie symmetries and preliminary classification. Explicit forms of equations are given for those admitting at least one intrinsic Lie symmetry. An algorithmic mechanism is also proposed to automate the symmetry calculation for fairly general DDEs via computer algebras.