Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.777925
Title: Parallel numerical methods for SDEs and applications
Author: Atallah, Nada
ISNI:       0000 0004 7963 6895
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
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Abstract:
Stochastic Differential Equations (SDEs) constitute an important mathematical tool with appli- cations in many areas of research such as fi physics and computer science. The analytical study of these equations is problematic, especially in the multi-dimensional case, for this reason, numerical techniques prove to be necessary to solve such equations. In this project, parallel numerical techniques for SDEs are studied. Two kinds of parallelism will be explored: in space and in time. Implementation of these techniques applied to several systems of SDEs will be realised (using C++ and MPI) and performance measures like speedup and efficiency will be investigated on medium-scale computer clusters. In the second part of the thesis, a major application area in the fi of computer and com- munication networks will be studied, that of second-order stochastic fl networks. Recently, interest has been growing in networks with large numbers of components, with application in diverse fi such as internet performance evaluation, the spread of computer viruses and biochemistry. Such models have such a large state space that discrete-state models are numer- ically infeasible due to the explosion in the size of the state space. Fluid approximations are therefore preferable and tend to be more accurate in large state spaces. In fl models, an integer counter is replaced by a real number representing a volume and the solution method becomes based on diff tial equations rather than on diff equations. Some analytical solutions are possible in special cases but in general, numerical methods are required. In this project, parallel numerical studies of second order fl networks will be conducted and re- sults in the context of the performance of computer and communication networks have been analysed, facilitating design improvement of their architecture.
Supervisor: Harrison, Peter Sponsor: Engineering and Physical Sciences Research Council ; Philippe Jabre Association
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.777925  DOI:
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