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第24卷第11期Vo.l24No.11荆楚理工学院学报JournalofJingchuUniversityofTechnology2009年11月Nov.2009[]2009-08-22[](1967-),,,:常微分方程在数学建模中的应用肖勇(,355000)[]文章深入探究了常微分方程在数学建模中的应用,阐述了常微分方程的发展和数学建模,并结合二者的特点与相关常微分方程在数学建模的例子,总结出常微分方程在数学建模的如何应用及学习过程中应注意的事项[]数学建模;常微分方程[]O241.81[]A[]1008-4657(2009)11-0050-031,,,,,,[1],,,,;,2,,,,,,[2],,,,,,,,,,,,,3,,50,,,3.1常微分方程在新产品推广模型中的应用,tx(t),,,tdx/dtx(t),N,,dx/dtN-x(t),dx/dt=kx(N-x),k0,,x(t)=N1+Ce-KNtdxdt=cN2ke-KNt(1+Ce-KNt)2d2xdt2=cK2N2e-KNt(Ce-KNt-1)(1+Ce-KNt)3,0x(t*)N,dx/dt0,x(t);x(t*)=N2,d2xdt2=0;x(t*)N2,d2xdt20;x(t*)N2,d2xdtt0,N,;N,;,,,,,20%~80%,;80%,,3.2常微分方程在动力学模型中的应用f=ma,,,m,=(t),k,,t,,tf=mg-k,mddt=mg-k,=mgk+ce-kmtt+,limt+(t)=mgklimt+(t)=mgk,,,mg/k,mg/k,3.3常微分方程在流体混合数学模型中的应用:At0,V0,Ax0()2(),1c1,tA:,tAx=x(t),c2,dt,Adx,,dx=c11dt-c22dtc2=xV0+(1-2)t,dxdt=-2V0+(1-2)tx+c11At,51(dxdt=-2V0+(1-2)tx+c11)x(0)=x03.4常微分方程在传染病模型中的应用1,tx(t),(),tt+t,x(t+t)-x(t)=x(t),tt=0x,dxdt=x,x(0)=x0,x(t)=x0et,t,x(t),,:,,,2:1)N,,,ts(t)i(t)(s(t)+i(t)=1)2)(),,s(t),Ni(t),Ns(t)i(t),xsiNi(t),Ndxdt=Nsi,Logisticdidt=i(1-i),i(0)=i0Logistici(t)=11+(1i0-1)e-ti=12di/dttm=-1ln(1i0-1),,,tm,,4,,,,,,,,,[][1].[M].:,1998.[2],,.[M].:,2003.[3].[M].:,2002.[:](63)52[4].[EB/OL].(2003-04-24).[5],.[J].,2006,28(5):254-255.[6],.[J].,2001(2):54-55.[:]StudyontheTourismDevelopmentStrategyofDazhouZHAONan1,ZHANGShu-lin1,DALing1,2(1CollegeofGeographicalSciences,ChongqingNormalUniversity,Chongqing,400047,China;2CollegeofHumanities,GuizhouUniversity,Guiyang,Guizhou,550025,China)Abstract:ThispapermadeadeepanalysistoDazhoutourismresources.Onthebasisofthis,thestrategydirectionofitstourismdevelopmentwasputforward,soastoprovidethereferencesfortherapid,deepandsustainabledevelopmentofDazhoutourism.Keywords:developmentstrategy;tourismdevelopmen;tDazhoucity(52)OrdinaryDifferentialEquationsinMathematicalModelingXIAOYong(NingdePolytechnic,Fu!an,Fujian,355000,China)Abstract:Thispaperfurtherexploredtheordinarydifferentialequationsinmathematicalmodelingapplications,anddescribedthedevelopmentofordinarydifferentialequationsandmathematicalmodeling,combinedwiththecharacteristicsofthetwoordinarydifferentialequationsandrelatedmathematicalmodelingexamples,summeduptheapplicationofordinarydifferentialequationsinmathematicalmodelingandsomequestionsthatweshouldpayattentiontoduringthelearningprocess.Keywords:mathematicalmodeling;ordinarydifferentialequations63
本文标题:常微分方程在数学建模中的应用
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