空間分?jǐn)?shù)階擴(kuò)散方程的幾種數(shù)值解法.pdf

1、獨(dú)創(chuàng)性聲明本人聲明所呈交的論文是我個(gè)人在導(dǎo)師指導(dǎo)下進(jìn)行的研究工作及取得的研究成果。盡我所知，除了文中特別加以標(biāo)注和致謝的地方外，論文中不包含其他人已經(jīng)發(fā)表或撰寫過(guò)的研究成果，也不包含為獲得寧夏大學(xué)或其它教育機(jī)構(gòu)的學(xué)位或證書而使用過(guò)的材料。與我一同工作的同志對(duì)本研究所做的任何貢獻(xiàn)均已在論文中作了明確的說(shuō)明并表示了謝意。研究生簽名：諍低；也時(shí)間：力∥降多月弓日關(guān)于論文使用授權(quán)的說(shuō)明本人完全了解寧夏大學(xué)有關(guān)保留、使用學(xué)位論文的規(guī)定，即：學(xué)校有

2、權(quán)保留送交論文的復(fù)印件和磁盤，允許論文被查閱和借閱，可以采用影印、縮印或掃描等復(fù)制手段保存、匯編學(xué)位論文。同意寧夏大學(xué)可以用不同方式在不同媒體上發(fā)表、傳播學(xué)位論文的全部或部分內(nèi)容。(保密的學(xué)位論文在解密后應(yīng)遵守此協(xié)議)研究生簽名：；多句掃刷謐各翥／章拭最JI、^o＼J時(shí)間：少／妒年莎月羅H時(shí)間：2o／z幺年∥月夕日AbstractFractionalorderdifferentialequationisaclassofdifferent

3、ialequationswhichisfromthepracticalproblemsAsanimportantpartofthetheoryofdifferentialequation，thestudyofitcanenrichmathematicaltheoryofdifferentialequation，ontheotherhand，itisalsoprovidemanymathematicalmodelsforthestudyo

4、fchemistrybiologyphysics，engineeringandeconomicphenomenonandtheprocessofmanyaspects，whichpromotetheresearchanddevelopmentofthesedisciplinesAsweknowcomparedwithintegerorderdifferentialequation，fractionalorderdifferentiale

5、quationislessperfectItisshortforscientificsolutionformulaAtpresentthestudyofitisstillinitsinfancyInordertothoroughlypromotetheresearchanddevelopmentoffractionalorderdifferentialequations，especiallytheresearchofnumericals

6、olution，itisnecessarytomakealotofWOrkInthispaperwemainlystudythenumericalmethodsforsolvingthespatialfractionaldiffusionequationThefractionalorderderivativeisGrfinwald—Letnikovdefinitionintermsofthefractionalorderderivati

7、veFirstlythesourceofthefractionalorderdifferentialequations，significance，researchstatusathomeandabroad，preliminaryknowledgeandthestructureofthisarticlearegivenSecondlythefractionaldiffusionequationofonedimensionalspaceis

8、studiedbyconstructingaweightedexplicitfinitedifferenceschemeAndmakinganalysisofthestabilityandconvergenceofthisformatFinallyanumericalexampleisgiventoverifytheaccuracyandreliabilityofformatAgain，thispaperdiscussestheone—

9、dimensionalwithfractionalordervariablecoefficientofthesourcetermspaceconvection—diffusionequationAkindofweightedimplicitfinitedifferenceschemeisconstructedbytakingtheweightedparameters=a／2Itisprovedthatthiskindofdifferen

10、ceschemeisunconditionalconvergenceFinallyanumericalexampleisgiventoveilfythereliabilityandaccuracyofthisformatAt1ast。akindoftwodimensionalspacialfractionalorderconvectiondiffusionwhichiSderivedfromtheporousmediaseepagepr

11、oblemsAnADI—CNdifferencemethodisconstructedforsolvingthiskindofequationInordertoimprovetheaccuracyRichardsonextrapolationmethodisusedtomaketheequationtosolvefurtherAttheend，twonumericalexamplesareprovidedtoverifytheeffec