
Accession Number : ADA324354
Title : Numerical Analysis of Evolution Equations.
Descriptive Note : Final rept. 1 May 9231 Oct 96,
Corporate Author : STANFORD UNIV CA
Personal Author(s) : Stuart, Andrew M.
PDF Url : ADA324354
Report Date : 14 APR 1997
Pagination or Media Count : 5
Abstract : The overall objective of this work is to analyze and design effective computational algorithms for the integration of evolution equations over long time intervals. Many models of physical significance are characterised by the property of 'sensitive dependence on initial conditions': small changes in the given data can make large changes in the detailed output of the model. Examples of such systems include weather or climate models in certain parameter regimes and turbulent flow problems. For such systems the effect of numerical approximation is not immediately clear. We may view numerical approximation as a small perturbation and the previous discussion indicates that this can nonetheless have a large effect on the detailed output from the model, over long time intervals. Thus it is important to know how to interpret data from such numerical simulations. Furthermore, in longtime integration, it is often crucial that the correct energy balance be used in the equation  be it dissipation or conservation. Thus it is important to design methods which replicate the energy balance in the equation under mild or no restrictions on the discretization parameters. These objective have been achieved and the following list of Awards, Invited Presentations, Graduated Students and Publications are all directly related to the support obtained through this grant.
Descriptors : *NUMERICAL ANALYSIS, *EVOLUTION(GENERAL), MATHEMATICAL MODELS, ALGORITHMS, OUTPUT, TIME INTERVALS, COMPUTATIONS, WEATHER, STUDENTS, PARAMETERS, ENERGY, TURBULENT FLOW, SENSITIVITY, LONG RANGE(TIME), INTEGRATION, APPROXIMATION(MATHEMATICS), PERTURBATIONS, EQUATIONS.
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE