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|Title: ||Higher order parallel splitting methods for parabolic partial differential equations|
|Authors: ||Taj, Malik Shahadat Ali|
|Advisors: ||Twizell, EH|
|Publication Date: ||1995|
|Publisher: ||Brunel University, School of Information Systems, Computing and Mathematics|
|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.|
|Description: ||This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.|
|Sponsorship: ||Government of Pakistan (Central Overseas Training Scholarship)|
|Appears in Collections:||Mathematics|
School of Information Systems, Computing and Mathematics Theses
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