perm filename JAN.ABS[BIB,CSR]1 blob sn#391592 filedate 1978-10-26 generic text, type C, neo UTF8

COMMENT ⊗ VALID 00003 PAGES C REC PAGE DESCRIPTION C00001 00001 C00002 00002 .REQUIRE "ABSTRA.CMD[BIB,CSR]" SOURCE FILE C00003 00003 .once center <<general instructions>> C00009 ENDMK C⊗; .REQUIRE "ABSTRA.CMD[BIB,CSR]" SOURCE FILE .every heading (January,1979 Reports,,{Page}) .at "∞" ⊂"%4α∞%*"⊃ .next page .once center <<general instructions>> %3MOST RECENT CS REPORTS - JANUARY 1979 @Listed below are abstracts of the most recent reports published by the Computer Science Department of Stanford University. @TO REQUEST REPORTS:##Check the appropriate places on the enclosed order form, and return the entire order form page (including mailing label) by January 12, 1979. In many cases we can print only a limited number of copies, and requests will be filled on a first come, first serve basis. If the code (FREE) is printed on your mailing label, you will not be charged for hardcopy. This exemption from payment is limited primarily to libraries. (The costs shown include all applicable sales taxes. PLEASE SEND NO MONEY NOW, WAIT UNTIL YOU GET AN INVOICE.) @ALTERNATIVELY: Copies of most Stanford CS Reports may be obtained by writing (about 2 months after MOST RECENT CS REPORTS listing) to NATIONAL TECHNICAL INFORMATION SERVICE, 5285 Port Royal Road, Springfield, Virginia 22161. Stanford Ph.D. theses are available from UNIVERSITY MICROFILMS, 300 North Zeeb Road, Ann Arbor, Michigan 48106. .begin nofill %4-------------------------------------------------------------------------------------%1 %3STAN-CS-79-691 THE CONSTRUCTION OF INITIAL DATA FOR HYPERBOLIC SYSTEMS FROM NONSTANDARD DATA %3Author:%1 Kenneth P. Bube↔(Thesis) .end @%3Abstract:%1@We study the first order systems of hyperbolic partial differential equations with periodic boundary conditions in the space variables for which complete initial data are not available. We suppose that we can measure %2u%1↑I , the first %2j%1 components of a solution %2u%1 of the system, perhaps with its time derivatives, but cannot measure %2u%2∩[II] , the rest of the components of %2u%1 , completely and accurately at any time level. Such problems arise in geophysical application where satelites are used to collect data. We consider two questions. How much information do we need to determine the solution %2u%1 uniquely in a way which depends continuously on the data? How do we use these data compuationally to obtain complete initial data at some time level? @We investigate several approaches to answering these questions. We show that under certain hypotheses %2u%1∩[II] at the initial time is determined uniquely by and depends continuously on the data obtained by measuring either %2u%1↑I over a whole time interval or %2u%1↑I and its first time derivative at the initial time, together ith either %2u%1∩[II] on a hyperplane in space of one lower dimension or a finite number of Fourier coefficients of %2u%1∩[II] at the initial time. Our results demonstrate that it is possible to reduce the data requirements of %2u%1∩[II] if sufficient information about %2u%2↑I is available. @One appliction we examine is the effect of the Coriolis term in the linearized shallow water equations on the possibility of recovering the wind fields from the geopotential height. @We present algorithms and computational results for these approaches for a model two-by-two system, and examine the method for intermittent updating currently being used in numerical weather prediction as a method for the assimilation of data. Our results suggest that the use of different frequencies of updating is important to avoid slow convergence. .begin nofill No. of pages: 119 Available in microfiche only. %4-------------------------------------------------------------------------------------%1