偏微分方程数值求解 Numerical Solutions of Partial Differential Equations ( 2009)

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1、AdvancedCoursesinMathematicsCRMBarcelonaCentredeRecercaMatemàticaManagingEditor:ManuelCastelletSilviaBertoluzzaSilviaFallettaGiovanniRussoChi-WangShuNumericalSolutionsofPartialDifferentialEquationsBirkhäuserBasel·Boston·BerlinAuthors:SilviaBertoluzzaGiovanniRussoIstit

2、utodiMatematicaApplicataeDipartimentodiMatematicaedInformaticaTecnologieInformatichedelC.N.R.UniversitàdiCataniav.Ferrata1VialeAndreaDoria627100Pavia95125CataniaItalyItalye-mail:silvia.bertoluzza@imati.cnr.ite-mail:russo@dmi.unict.itSilviaFallettaChi-WangShuDipartimen

3、todiMatematicaDivisionofAppliedMathematicsPolitecnicodiTorinoBrownUniversityCorsoDucadegliAbruzzi,24Providence,RI0291210129TorinoUSAItalye-mail:shu@dam.brown.edue-mail:silvia.falletta@polito.it2000MathematicalSubjectClassification35-99,65-99LibraryofCongressControlNumb

4、er:2008940758BibliographicinformationpublishedbyDieDeutscheBibliothekDieDeutscheBibliothekliststhispublicationintheDeutscheNationalbibliografie;detailedbibliographicdataisavailableintheInternetat.ISBN978-3-7643-8939-0BirkhäuserVerlagAG,Basel–Boston–B

5、erlinThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinotherways,andstorageindatabanks.Foranykindofusepe

6、rmissionofthecopyrightownermustbeobtained.©2009BirkhäuserVerlag,P.O.Box133,CH-4010Basel,SwitzerlandPartofSpringerScience+BusinessMediaPrintedonacid-freepaperproducedfromchlorine-freepulp.TCF∞PrintedinGermanyISBN978-3-7643-8939-0e-ISBN978-3-7643-8940-6987654321www.birk

7、hauser.chContentsForewordixIWaveletsandPartialDifferentialEquationsSilviaBertoluzzaandSilviaFalletta1Introduction..................................31WhatisaWavelet?51.1MultiresolutionAnalysis........................51.1.1ExampleI:TheHaarBasis..................131.1.2Ex

8、ampleII:B-Splines.....................141.1.3ExampleIII:Daubechies’sWavelets.............141.1.4ExampleIV:TheSchauderBasis..