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" Higher order parallel splitting methods for parabolic partial differential equations "
Taj, Malik Shahadat Ali
Twizell, E. H.
Document Type
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Latin Dissertation
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Record Number
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828098
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Doc. No
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TLets295189
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Main Entry
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Taj, Malik Shahadat Ali
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Title & Author
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Higher order parallel splitting methods for parabolic partial differential equations\ Taj, Malik Shahadat AliTwizell, E. H.
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College
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Brunel University
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Date
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1995
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student score
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1995
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Degree
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Thesis (Ph.D.)
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Abstract
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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.
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Subject
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Heat equations
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Added Entry
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Twizell, E. H.
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Added Entry
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Brunel University
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