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Title: On the fast and accurate computer solution of partial differential systems
Author: Hill, Michael T.
Awarding Body: University of St Andrews
Current Institution: University of St Andrews
Date of Award: 1974
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Two methods are presented for use on an electronic computer for the solution of partial differential systems. The first is concerned with accurate solutions of differential equations. It is equally applicable to ordinary differential equations and partial differential equations, and can be used for parabolic, hyperbolic or elliptic systems, and also for non-linear and mixed systems. It can be used in conjunction with existing schemes. Conversely, the method can be used as a very fast method of obtaining a rough solution of the system. It has an additional advantage over traditional higher order methods in that it does not require extra boundary conditions. The second method is concerned with the acceleration of the convergence rate in the solution of hyperbolic systems. The number of iterations has been reduced from tens of thousands with the traditional Lax-Wendroff methods to the order of twenty iterations. Analyses for both the differential and the difference systems are presented. Again the method is easily added to existing programs. The two methods may be used together to give one fast and accurate method.
Supervisor: Wirz, H. J. ; Curle, S. N. Sponsor: Science Research Council ; Von Karman Institute for Fluid Dynamics
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA377.H5 ; Differential equations, Partial