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Title: Higher-order finite-difference methods for partial differential equations
Author: Cheema, Tasleem Akhter
ISNI:       0000 0001 3530 8484
Awarding Body: Brunel University
Current Institution: Brunel University
Date of Award: 1997
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This thesis develops two families of numerical methods, based upon rational approximations having distinct real poles, for solving first- and second-order parabolic/ hyperbolic partial differential equations. These methods are thirdand fourth-order accurate in space and time, and do not require the use of complex arithmetic. In these methods first- and second-order spatial derivatives are approximated by finite-difference approximations which produce systems of ordinary differential equations expressible in vector-matrix forms. Solutions of these systems satisfy recurrence relations which lead to the development of parallel algorithms suitable for computer architectures consisting of three or four processors. Finally, the methods are tested on advection, advection-diffusion and wave equations with constant coefficients.
Supervisor: Twizell, E. H. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Advection equations; Hyperbolic equations Mathematics Applied mathematics