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DC Field | Value | Language |
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dc.contributor.advisor | Twizell, EH | - |
dc.contributor.author | Taj, Malik Shahadat Ali | - |
dc.date.accessioned | 2011-09-13T11:19:05Z | - |
dc.date.available | 2011-09-13T11:19:05Z | - |
dc.date.issued | 1995 | - |
dc.identifier.uri | http://bura.brunel.ac.uk/handle/2438/5780 | - |
dc.description | This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University. | en_US |
dc.description.abstract | The thesis develops two families of numerical methods, based upon new rational approximations to the matrix exponential function, for solving second-order parabolic partial differential equations. These methods are L-stable, third- and fourth-order accurate in space and time, and do not require the use of complex arithmetic. In these methods second-order spatial derivatives are approximated by new difference approximations. Then parallel algorithms are developed and tested on one-, two- and three-dimensional heat equations, with constant coefficients, subject to homogeneous boundary conditions with discontinuities between initial and boundary conditions. The schemes are seen to have high accuracy. A family of cubic polynomials, with a natural number dependent coefficients, is also introduced. Each member of this family has real zeros. Third- and fourth-order methods are also developed for one-dimensional heat equation subject to time-dependent boundary conditions, approximating the integral term in a new way, and tested on a variety of problems from the literature. | en_US |
dc.description.sponsorship | Government of Pakistan (Central Overseas Training Scholarship) | en_US |
dc.language.iso | en | en_US |
dc.publisher | Brunel University, School of Information Systems, Computing and Mathematics | - |
dc.relation.ispartof | School of Information Systems, Computing and Mathematics | - |
dc.relation.uri | http://bura.brunel.ac.uk/bitstream/2438/5780/1/FulltextThesis.pdf | - |
dc.title | Higher order parallel splitting methods for parabolic partial differential equations | en_US |
dc.type | Thesis | en_US |
Appears in Collections: | Dept of Mathematics Theses Mathematical Sciences |
Files in This Item:
File | Description | Size | Format | |
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FulltextThesis.pdf | 3.31 MB | Adobe PDF | View/Open |
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