一類(lèi)非單調(diào)守恒性沙丘問(wèn)題的擬小波解.pdf

1、合肥工業(yè)大學(xué)碩士學(xué)位論文一類(lèi)非單調(diào)守恒性沙丘問(wèn)題的擬小波解姓名：楊巍申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：林京20090401Thequasi—waveletsolutionstoanonmonotoneconservationlawforduneproblemsAbstractWaveletnumericalmethodsarewidelyappliedtothenonlinearpartialequations，ofwhicht

2、hequasi—waveletsenjoyboththegloballyhighaccuracyandthelocallystabilityInthethesisweapplythequasi—waveletsnumericalmethodtoaclassofnonlinearevolutionequationsthatreferstoinstabilitiesinlandformsofdunes，whichoccurthroughth

3、einteractionofaturbulentflowwithanerodiblesubstrate，andwhichwasshownviolatingtheconservationlawThenumericalmethodsinthisthesisareasfollows：weapplythequasiwaveletschemeandthefourth—orderRunge—Kuttamethodrespectivelytodisc

4、retizethespatialderivativesandthetemporalderivative，whilemakeuseoftheNewton—SimpsonintegralmethodtodiscretizethederivativeofnonlocaloperatorTheadvantageofoursisthatduetotheGaussregularizerinthequasiwaveletbasis，thenumeri

5、calprocessconvergesmuchfastThenumericalresultsalsoconfirmtheviolenceofthemaximumprincipleinthenumericalsolutionsInthethesiswealsosystematicallydiscussthetheoryofwaveletanalysisandquasiwaveletmethodKeywords：wavelet，quasiw