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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/13492

Title: High-order finite difference methods for partial differential equations
Authors: Bowen, Matthew K.
Issue Date: 2005
Publisher: © Matthew Bowen
Abstract: General n-point formulae for difference operators and their errors are derived in terms of elementary symmetric functions. These are used to derive high-order, compact and parallelisable finite difference schemes for the decay-advection-diffusion and linear damped Korteweg-de Vnes equations. Stability calculations are presented and the speed and accuracy of the schemes is compared to that of other finite difference methods in common use. Appendices contain useful tables of difference operators and errors and present a stability proof for quadratic inequalities. For completeness, the appendices conclude with the standard Thomas method for solving tri-diagonal systems.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.
URI: https://dspace.lboro.ac.uk/2134/13492
Appears in Collections:PhD Theses (Maths)

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