Sensitivity analysis and computation for partial differential equations /

The development of practical numerical methods for simulation of partial differential equations leads to problems of convergence, accuracy and efficiency. Verification of a computational algorithm consists in part of establishing a convergence theory for the discretized equations. It is well known that the long time behavior of a system may not be captured even by "convergent" approximating methods and additional requirements must be placed on the scheme to ensure the discretized equations capture the correct asymptotic behavior. Even on finite intervals, there are always uncertainties in the problem data that can be a source of difficulty for accurate simulation of nonlinear problems. These uncertainties lead to uncertainty in the computed results and should be considered as part of the verification step. This research gives preliminary results showing how sensitivity analysis can be used to provide a practical precursor to dynamic transitions and quantify numerical uncertainty in simulations of nonlinear parabolic partial differential equations.Photocopy."March 14, 2008.""Final Technical Report : May 1, 2007 -- November 30, 2007."Includes bibliograpic references (pages 10-12).The development of practical numerical methods for simulation of partial differential equations leads to problems of convergence, accuracy and efficiency. Verification of a computational algorithm consists in part of establishing a convergence theory for the discretized equations. It is well known that the long time behavior of a system may not be captured even by "convergent" approximating methods and additional requirements must be placed on the scheme to ensure the discretized equations capture the correct asymptotic behavior. Even on finite intervals, there are always uncertainties in the problem data that can be a source of difficulty for accurate simulation of nonlinear problems. These uncertainties lead to uncertainty in the computed results and should be considered as part of the verification step. This research gives preliminary results showing how sensitivity analysis can be used to provide a practical precursor to dynamic transitions and quantify numerical uncertainty in simulations of nonlinear parabolic partial differential equations.Report prepared by Department of Mathematical Sciences, Montana State University, Bozeman, Montana, under contract no.Mode of access: Internet