Date of Award


Degree Type


Degree Name

Doctor of Philosophy


Several calculations of interactions between particles suspended in fluid are first described. In order to complete these calculations efficiently, several facilities that the present version of Maple does not provide are identified. These include the efficient computation of series solutions of ordinary differential equations, the management of large expressions and the convenient solution of polynomial equations in terms of a set of algebraic extensions dependent over the rationals. These facilities are developed and the calculations carried through to completion. A feature of the computations is the solution of ordinary differential equations to high accuracy by series methods. The mathematical and programming development of Maple packages to solve polynomial equations, and to obtain many terms of series solutions to ordinary differential equations are described. The series-solution package applies to linear ordinary differential equations of arbitrary order about ordinary points and regular singular points.



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