延迟时间分数阶扩散方程有限差分方法的稳定性

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1、Æ“Ò10530ÆÒ201510111148©aÒO241:81—?a¬ÆØ©ò´žm©ê*Ñ•§k•©•{•½5Æž<“r•P“©á²Çƶ¡êƆOŽ‰ÆÆƉ;’êÆïÄ••‡©•§êŠ)•{˜lco›Fò´žm©ê*Ñ•§k•©•{•½5Æž<“r•P“©á²Çƶ¡êƆOŽ‰ÆÆƉ;’êÆïÄ••‡©•§êŠ•{Æž?OnÆa¬Æǃü‰ŒÆØ©JFÏ2018-4-12Stabilityofnitedifferencemethodfordelaytimefractionaldiffusioneq

2、uationCandidateZhiqiangWangSupervisorProfessorLipingWenCollegeSchoolofMathematicsandComputationalScienceProgramMathematicsSpecializationNumericalMethodsforDierentialEquationsDegreeMasterofScienceUniversityXiangtanUniversityDateApril12th,2018Á‡©•ÄXeò´žm©ê*Ñ•§Ð>Š¯KêŠ){8>>>>@u(x;t

3、)@2u(x;t)><@t+a@x2=bu(x;t)+p(x;t)§0>>>>:u(0;t)=k0(t)§u(L;t)=k1(t)§00§T>0§¼êp(x;t)!K(x;t)!k0(t)!k1(t)Ñ´®•…ëY.@t•Caputo©êê.©òCaputo©êê=z•Riemann-Liouville©êÈ©§2

4、^Lubich‚5õÚ{éRiemann-Liouville©êÈ©?1lѧ˜mCþê

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6、¥%©•{?1lѧ¦)þã¯Kꊕ{¿y²T•{•½5.?1˜êŠÁ§Ù(J?˜ÚyT•{Œ159nØ©Û(5.'…c:k•©¶©ê‡©•§¶*Ñ•§¶•½5©ÛIIAbstractInthispaper,weconsiderthenumericalsolutionoftheinitialboundaryvalueproblemofthedelaytimefractionaldiusionequation8>>>>@u(x;t)@2u(x;t)><@t+a@x2=bu(x;t)+p(x;t);0

7、x;t)=K(x;t);06x6L;6t60;>>>>>:u(0;t)=k0(t);u(L;t)=k1(t);00§T>0,p(x;t),K(x;t),k0(t)andk1(t)arecontinuousfunctions.@u(x;t)isCaputofractionalderivativewithorder.Wetransformedthefractionalderivative@tofCaputointoRiemann-Liouvillefractionalintegral,thenweuseLubich'sli

8、nearmultistepmethodtodiscreteRiemann-Liouvillefractionalintegralandsecond-ordercentraldierenceisusedforthespacederivative.Weobtainthenumericalmethodforsolvingthatproblemsandprovethestabilityofmethod.Thefeasibilityofthemethodisveriedbynumericalexperiments.Keywords:nitedierence;f

9、ractionalorderdierentialequation;diusionequation;sta-bilityanalysisIII8¹1˜ÙÚó11.1ïĵ......................................11.2ý•£......................................71.3©̇óŠ..................................91Ùk•©•{•½5©Û102.1¯K£ã......................................102.

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