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Determining the symmetries of initial-value problems.

Watts, Richard. (2005) Determining the symmetries of initial-value problems. Doctoral thesis, University of Surrey (United Kingdom)..

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Although symmetry analysis provides a powerful tool for solving differential equations, it has not proved to be as successful in the treatment of initial-value and boundary-value problems. A possible reason for this is the belief that the set of symmetries of an initial-value problem is a subset of the symmetries of the associated governing differential equation. It was recently shown that this is, in fact, not the case and a method introduced for constructing the symmetries of a class of initial-value problems using Taylor series. The present thesis extends this method to arbitrary-order regular ordinary differential equations subject to both an arbitrary-order single initial condition and an arbitrary linear combination of single initial conditions. Furthermore, a practical method for dealing with a class of initial-value problems that possess a regular singularity is developed, through the use of the Frobenius method.

Item Type: Thesis (Doctoral)
Divisions : Theses
Authors :
Date : 2005
Contributors :
Depositing User : EPrints Services
Date Deposited : 09 Nov 2017 12:17
Last Modified : 09 Nov 2017 14:45

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