13404.擬小波方法求解時(shí)間變分?jǐn)?shù)階偏微分方程

1、分學(xué)校代碼10542擬小波方法求解時(shí)間變分?jǐn)?shù)階偏微分方程QuasiWaveletforthetimevariableorderfractionalpartialdifferentialequation研究生姓名：室!!堊』指導(dǎo)教師姓名、職稱：徐大塾絲學(xué)科專業(yè)：計(jì)算數(shù)堂研究方向：偏垡分壅堡蔓生魚豎湖南師范大學(xué)學(xué)位評(píng)定委員會(huì)辦公室二零一六年五月ABSTRACTIntheresearchoffluidmechanics，biologyfina

2、nce，chemicalprocess，S—tochasticprocess，materialscienceandSOon，thefractionalorderpartialdifferentialequationappearsfrequentlyInrecentyears，withthedevelopmentofresearchproblems，thefractionalorderpartialdifferentialequation

3、shavebeenextendedtothevariableorderfractionalpartialdifferentialequationsbymanyexpertsandscholarsButbecauseofthevariableorderfractionalpartialdifferentialequation，thenumericalsolutionismoredifficulttosolve，SOthestudyofth

4、enumericalsolutionofthedifferentialequationwithvariableorderfractionalislessAtpresent，maindomesticandinternationalresearcherSonthisproblemareasfollows：Chen，CM，F(xiàn)Liu[1，2，3】，Shen，s■[8】)Soon，C^z，F(xiàn)MConbra，MHKobayashi[11]，Comb

5、ra，F(xiàn)M[12]，Zhuang，P，Liu，F(xiàn)，VAnh[131，Sun，HⅣ，WChen，YChen[14]Inthesepapers，hardlyanyoneusethequasiwaveletmethodtosolvethevariableorderfractionaldifferentialequationsThispapermainlydiscussesaclassoftimevariableorderfractionalp

6、ar—tialdifferentialequationsbyusingthequasiwaveletmethodThisthesisisdividedintosixchaptersThefirstandthetwochaptermainlyintroducethedevelopmentofthevariableorderfractionalpartialdifferentialequations，theresearchstatusath

7、omeandabroadaswellasthedefinitionofsomevari—ablefractionalorderderivativesThethirdchapterstudiestheFullydiscreteschemesoftheEulercompactdifferenceofthetimevariableorderfractionalcableequationanditsstabilityandconvergence

8、ThefourthchaptergivesabriefintrodutiontothetheoryofthequasiwaveletfunctionandthederivativeapproximationThefifthchapterillustratestheEulertimesemidiscreteschemeofthetimevariableorderfractionalcableequationandtheEulerquasi