Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.586356
Title: Accelerated numerical schemes for deterministic and stochastic partial differential equations of parabolic type
Author: Hall, Eric Joseph
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2013
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Abstract:
First we consider implicit finite difference schemes on uniform grids in time and space for second order linear stochastic partial differential equations of parabolic type. Under sufficient regularity conditions, we prove the existence of an appropriate asymptotic expansion in powers of the the spatial mesh and hence we apply Richardson's method to accelerate the convergence with respect to the spatial approximation to an arbitrarily high order. Then we extend these results to equations where the parabolicity condition is allowed to degenerate. Finally, we consider implicit finite difference approximations for deterministic linear second order partial differential equations of parabolic type and give sufficient conditions under which the approximations in space and time can be simultaneously accelerated to an arbitrarily high order.
Supervisor: Gyongy, Istvan; Sabanis, Sotirios Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.586356  DOI: Not available
Keywords: Richardson's method ; acceleration of convergence ; extrapolation to the limit ; finite difference schemes ; stochastic partial differential equations ; partial differential equations ; parabolic type ; degenerate parabolic type ; Cauchy problem
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