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Title: Higher order parallel splitting methods for parabolic partial differential equations
Author: Taj, Malik Shahadat Ali
ISNI:       0000 0001 3496 2070
Awarding Body: Brunel University
Current Institution: Brunel University
Date of Award: 1995
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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.
Supervisor: Twizell, E. H. Sponsor: Government of Pakistan (Central Overseas Training Scholarship)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Heat equations