Return to search

Accelerated numerical schemes for deterministic and stochastic partial differential equations of parabolic type

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.

Identiferoai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:586356
Date January 2013
CreatorsHall, Eric Joseph
ContributorsGyongy, Istvan; Sabanis, Sotirios
PublisherUniversity of Edinburgh
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Sourcehttp://hdl.handle.net/1842/8038

Page generated in 0.0019 seconds