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1、Runge-kutta2010–5–27SeveralKindsofRunge-KuttaMethodsforFractionalDifferentialEquationsCandidateSupervisorCollegeProgramSpecialityDegreeUniversityDateYunfeiLiProfessorXuenianCaoMathematicsandComputationalScienceComputationalMathematicsNumericalSolutionofFractionalDifferentialEqu
2、ationsMasterofScienceXiangtanUniversityApril18th,2010,,,,,L-Runge-KuttaRiemann-Liouville,,RadauIA,,L-.Runge-Kutta.Runge-KuttaIL-Runge-KuttaLobattaIIICAbstractBasedonahighorderapproximationofL-stableRunge-KuttamethodsforRiemann-Liouvillefractionaldirivatives,aclassofhig
3、h-orderL-stableRunge-Kuttamethodsforsolvingthenonlinearfractionaldifferentialequationsiscon-structedinthispaper.Consistency,convergence,andstabilityanalysisofthesemethodsaregiven.Innumericalexperiments,fractionalRadauIAmethodsandLobattoIIICmethodsandsingly-diagonalimplicitRunge
4、-Kuttamethodscom-biningtheshortmemoryprinciplearechosen.Thesemethodsareefficientforsolvingnonlinearfractionaldifferentialequations.Keywords:Fractionaldifferentialequation;L-stableRunge-Kuttamethod;consistency;convergence;stability;shortmemoryprincipleII............................
5、....................1L-Runge-Kutta.................2§2.1§2.2§2.3§2.4...........................................4..........................................4...........................................6..........................................8................................
6、...........11...................................................22.....................................................23.........................................................25III.,[1]Abel(GorenfloVessela,1991)[2],(RossikhinShitikova,1997)[3],(Benson,WheatcraftMeersc
7、hert,2000a,b)[4],.(Wyss,2000)[5],,,,.,,.,.K.Diethelm,N.J.FordA.D.Freed[6]-.,,[7],[9][10].Lubich[8]Runge-KuttaAbel-Volterra.Lubich,[1],[11]Runge–Kutta,[13].RadauIIA.,,[12],,,.,.[14]Riemann-Liouville.,FordSimpson[15].,L-L-Runge-KuttaRunge-K
8、utta.,(,L-L-RK),Runge-Kutta,LobattoIIICRadauIA,,Run
