非线性Volterra-Fredholm积分微分.pdf

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1、—?µúmš‚5Volterra-FredholmÈ©‡©•§êŠ){NumericalSolutionMethodsforNonlinearVolterra-FredholmIntegro-DierentialEquations£žöÞŒÆnÆa¬ÆØ©¤£X!¤¤µnÆêÆX;’µA^êÆïÄ)µx?B•“µ4JÇO˜coÆØ©M5(²Ø©´·‡<3“•e?1óŠïÄ9ïĤJ"Ø©¥ØAO±I5Ú—/•§Ø•¹Ù¦<½Ù§Å®²uL½>LïĤJ"é©ïĉÑz‡<Ú8N§

2、þ®3Ø©¥±²(•ªI²"<¿£(²{ÆI?d<«ú"Ø©Šö¶µFϵcFÆØ©¦^Ç`²<ÇöތƕÆØ©>fÚ’Ÿ©§#NØ©Ú/¶ÆŒòÆØ©ܽܩSN?k'êâ¥?1u¢§Œ±æ^K

3、FFϵcFöÞŒÆa¬ÆØ©ÁÁÁ‡‡‡š‚5VolterraõFredholmÈ©‡©•§´˜a~„È©‡©•§.êÆ!ÔnÆÚó§þNõ¯KŒ±8(•ùa•§.duÙA^‰Œ2,¦Ta•§Cq)õc5˜†´Æâ.ïÄ9:.©•ÄXeš‚5Volterra-FredholmÈ©‡©•§êŠ){:(RR0tbX(t)+Q(t)X(t)+1ak1(s;t)F(X(s))ds+2ak2(s;t)G(X(s))ds=Y(t)X(a)=X0;atb:kÏL‚5C†r«m[a;b]C†[1;1],2A^Clenshaw-

4、CurtisêŠÈ©•{Úpꊇ©•{lÑC†È©‡©•§.©„?ØÏL镧?1È©¿†È©^Sr‡©È©•§=z•È©•§,lmz•§¦)L§.©©•üÙ,̇SNSüXe.1˜Ùk0©‡^êƽÂÚƒ'•£,20Ø©ïĵڿ±98cÆâ.éš‚5VolterraõFredholmÈ©‡©•§ïÄyG,•0©̇ïÄSNÚÙ!Sü.1Ùk?ØòClenshaw-CurtisêŠÈ©•{A^È©Žf¥,,2퇩ŽflÑ/ª.X?ØÏLéÈ©‡©•§?1È©¿†È©^S,=z•˜‡#

5、Volterra-FredholmÈ©•§2?1¦).•‰ÑêŠ~f,`²©JÑ•{k5.'''………ccc:š‚5VolterraõFredholmÈ©‡©•§;Clenshaw-Curtis¦È•{;õ‘ªŠ;Chebyshevõ‘ª;IöÞŒÆa¬ÆØ©AbstractNonlinearVolterra-Fredholmintegro-dierentialequationisakindofim-portantintegro-dierentialequation,whicharisesfrommathematics,p

6、hysicsandengineering,etc.Numericalsolutionmethodsfortheequationhavebeenattractingalotofattentionduetoitsextensiveapplicationsinmathematicsandengineering.Inthethesis,weconsidernumericalsolutionmethodsfornonlinearVolterra-Fredholmintegro-dierentialequationsdenedonanitein

7、terval[a;b]:(RR0tbX(t)+Q(t)X(t)+1ak1(s;t)F(X(s))ds+2ak2(s;t)G(X(s))ds=Y(t)X(a)=X0;atb:Firstlywetransformtheinterval[a;b]to[1;1]byusingcertainlineartrans-formation.WethenapplytheClenshaw-Curtisquadraturestodiscretizetheintegraloperatorsandhighordernumericaldierentiat

8、ionmethodtodiscretizetherstorderderivative.Wealsointroduceamethodtotransformtheintegro-dierent