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" Higher order parallel splitting methods for parabolic partial differential equations "


Document Type : Latin Dissertation
Record Number : 828098
Doc. No : TLets295189
Main Entry : Taj, Malik Shahadat Ali
Title & Author : Higher order parallel splitting methods for parabolic partial differential equations\ Taj, Malik Shahadat AliTwizell, E. H.
College : Brunel University
Date : 1995
student score : 1995
Degree : Thesis (Ph.D.)
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.
Subject : Heat equations
Added Entry : Twizell, E. H.
Added Entry : Brunel University
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TLets295189_70397.pdf
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