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Complete symmetry groups : a connection between some ordinary differential equations and partial differential equations.
The concept of complete symmetry groups has been known for some time in applications to ordinary differential equations. In this Thesis we apply this concept to partial differential equations. For any 1+1 linear evolution ...
Algebraic properties of ordinary differential equations.
In Chapter One the theoretical basis for infinitesimal transformations is presented with particular emphasis on the central theme of this thesis which is the invariance of ordinary differential equations, and their first ...
Lie group analysis of exotic options.
Exotic options are derivatives which have features that makes them more complex than vanilla traded products. Thus, finding their fair value is not always an easy task. We look at a particular example of the exotic options ...
Singularity and symmetry analysis of differential sequences.
We introduce the notion of differential sequences generated by generators of sequences. We discuss the Riccati sequence in terms of symmetry analysis, singularity analysis and identification of the complete symmetry group ...