matlab中ode45函数编写文档格式.docx

matlab中ode45函数编写文档格式.docx

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Mass'

propertytoafunctionhandle

%MASSifMASS（T,Y）returnsthevalueofthemassmatrix.Ifthemassmatrix

%isconstant,thematrixcanbeusedasthevalueofthe'

option.If

%themassmatrixdoesnotdependonthestatevariableYandthefunction

%MASSistobecalledwithoneinputargumentT,set'

MStateDependence'

to

%'

none'

.ODE15SandODE23Tcansolveproblemswithsingularmassmatrices.

%

%[TOUT,YOUT,TE,YE,IE]=ODE45（ODEFUN,TSPAN,Y0,OPTIONS）withthe'

Events'

%propertyinOPTIONSsettoafunctionhandleEVENTS,solvesasabove

%whilealsofindingwherefunctionsof（T,Y）,calledeventfunctions,

%arezero.Foreachfunctionyouspecifywhethertheintegrationis

%toterminateatazeroandwhetherthedirectionofthezerocrossing

%matters.ThesearethethreecolumnvectorsreturnedbyEVENTS:

%[VALUE,ISTERMINAL,DIRECTION]=EVENTS（T,Y）.FortheI-theventfunction:

%VALUE（I）isthevalueofthefunction,ISTERMINAL（I）=1iftheintegration

%istoterminateatazeroofthiseventfunctionand0otherwise.

%DIRECTION（I）=0ifallzerosaretobecomputed（thedefault）,+1ifonly

%zeroswheretheeventfunctionisincreasing,and-1ifonlyzeroswhere

%theeventfunctionisdecreasing.OutputTEisacolumnvectoroftimes

%atwhicheventsoccur.RowsofYEarethecorrespondingsolutions,and

%indicesinvectorIEspecifywhicheventoccurred.

%SOL=ODE45（ODEFUN,[T0TFINAL],Y0...）returnsastructurethatcanbe

%usedwithDEVALtoevaluatethesolutionoritsfirstderivativeat

%anypointbetweenT0andTFINAL.ThestepschosenbyODE45arereturned

%inarowvectorSOL.x.ForeachI,thecolumnSOL.y（:

I）contains

%thesolutionatSOL.x（I）.Ifeventsweredetected,SOL.xeisarowvector

%ofpointsatwhicheventsoccurred.ColumnsofSOL.yearethecorresponding

%solutions,andindicesinvectorSOL.iespecifywhicheventoccurred.

%Example

%[t,y]=ode45（@vdp1,[020],[20]）;

%plot（t,y（:

1））;

%solvesthesystemy'

=vdp1（t,y）,usingthedefaultrelativeerror

%tolerance1e-3andthedefaultabsolutetoleranceof1e-6foreach

%component,andplotsthefirstcomponentofthesolution.

%ClasssupportforinputsTSPAN,Y0,andtheresultofODEFUN（T,Y）:

%float:

double,single

%Seealso

%otherODEsolvers:

ODE23,ODE113,ODE15S,ODE23S,ODE23T,ODE23TB

%implicitODEs:

ODE15I

%optionshandling:

ODESET,ODEGET

%outputfunctions:

ODEPLOT,ODEPHAS2,ODEPHAS3,ODEPRINT

%evaluatingsolution:

DEVAL

%ODEexamples:

RIGIDODE,BALLODE,ORBITODE

%functionhandles:

FUNCTION_HANDLE

%NOTE:

%TheinterpretationofthefirstinputargumentoftheODEsolversand

%somepropertiesavailablethroughODESEThavechangedinMATLAB6.0.

%Althoughwestillsupportthev5syntax,anynewfunctionalityis

%availableonlywiththenewsyntax.Toseethev5help,typein

%thecommandline

%moreon,typeode45,moreoff

%Thisportiondescribesthev5syntaxofODE45.

%[T,Y]=ODE45（'

F'

TSPAN,Y0）withTSPAN=[T0TFINAL]integratesthe

%systemofdifferentialequationsy'

=F（t,y）fromtimeT0toTFINALwith

%initialconditionsY0.'

isastringcontainingthenameofanODE

%file.FunctionF（T,Y）mustreturnacolumnvector.Eachrowin

%solutionarrayYcorrespondstoatimereturnedincolumnvectorT.To

%obtainsolutionsatspecifictimesT0,T1,...,TFINAL（allincreasing

%oralldecreasing）,useTSPAN=[T0T1...TFINAL].

TSPAN,Y0,OPTIONS）solvesasabovewithdefault

%integrationparametersreplacedbyvaluesinOPTIONS,anargument

%createdwiththeODESETfunction.SeeODESETfordetails.Commonly

%usedoptionsarescalarrelativeerrortolerance'

（1e-3by

%default）andvectorofabsoluteerrortolerances'

（all

%components1e-6bydefault）.

TSPAN,Y0,OPTIONS,P1,P2,...）passestheadditional

%parametersP1,P2,...totheODEfileasF（T,Y,FLAG,P1,P2,...）（see

%ODEFILE）.UseOPTIONS=[]asaplaceholderifnooptionsareset.

%ItispossibletospecifyTSPAN,Y0andOPTIONSintheODEfile（see

%ODEFILE）.IfTSPANorY0isempty,thenODE45callstheODEfile

%[TSPAN,Y0,OPTIONS]=F（[],[],'

init'

）toobtainanyvaluesnotsupplied

%intheODE45argumentlist.Emptyargumentsattheendofthecalllist

%maybeomitted,e.g.ODE45（'

）.

=F（t,y）withamassmatrixMthatis

%nonsingular.UseODESETtosetMassto'

M'

'

M（t）'

or'

M（t,y）'

ifthe

%ODEfileiscodedsothatF（T,Y,'

mass'

）returnsaconstant,

%time-dependent,ortime-andstate-dependentmassmatrix,respectively.

%ThedefaultvalueofMassis'

.ODE15SandODE23Tcansolveproblems

%withsingularmassmatrices.

%[T,Y,TE,YE,IE]=ODE45（'

TSPAN,Y0,OPTIONS）withtheEventspropertyin

%OPTIONSsetto'

on'

solvesasabovewhilealsolocatingzerocrossings

%ofaneventfunctiondefinedintheODEfile.TheODEfilemustbe

%codedsothatF（T,Y,'

events'

）returnsappropriateinformation.See

%ODEFILEfordetails.OutputTEisacolumnvectoroftimesatwhich

%eventsoccur,rowsofYEarethecorrespondingsolutions,andindicesin

%vectorIEspecifywhicheventoccurred.

%SeealsoODEFILE

%ODE45isanimplementationoftheexplicitRunge-Kutta（4,5）pairof

%DormandandPrincecalledvariouslyRK5（4）7FM,DOPRI5,DP（4,5）andDP54.

%Itusesa"

free"

interpolantoforder4communicatedprivatelyby

%DormandandPrince.Localextrapolationisdone.

%DetailsaretobefoundinTheMATLABODESuite,L.F.Shampineand

%M.W.Reichelt,SIAMJournalonScientificComputing,18-1,1997.

%MarkW.ReicheltandLawrenceF.Shampine,6-14-94

%Copyright1984-2009TheMathWorks,Inc.

%$Revision:

5.74.4.10$$Date:

2009/04/2103:

24:

15$

solver_name='

ode45'

;

%Checkinputs

ifnargin<

4

options=[];

ifnargin<

3

y0=[];

2

tspan=[];

1

error（'

MATLAB:

ode45:

NotEnoughInputs'

...

'

Notenoughinputarguments.SeeODE45.'

）;

end

end

end

%Stats

nsteps=0;

nfailed=0;

nfevals=0;

%Output

FcnHandlesUsed=isa（ode,'

function_handle'

output_sol=（FcnHandlesUsed&

&

（nargout==1））;

%sol=odeXX（...）

output_ty=（~output_sol&

（nargout>

0））;

%[t,y,...]=odeXX（...）

%Theremightbenooutputrequested...

sol=[];

f3d=[];

ifoutput_sol

sol.solver=solver_name;

sol.extdata.odefun=ode;

sol.extdata.options=options;

sol.extdata.varargin=varargin;

end

%Handlesolverarguments

[neq,tspan,ntspan,next,t0,tfinal,tdir,y0,f0,odeArgs,odeFcn,...

options,threshold,rtol,normcontrol,normy,hmax,htry,htspan,dataType]=...

odearguments（FcnHandlesUsed,solver_name,ode,tspan,y0,options,varargin）;

nfevals=nfevals+1;

%Handletheoutput

ifnargout>

0

outputFcn=odeget（options,'

OutputFcn'

[],'

fast'

else

@odeplot,'

outputArgs={};

ifisempty（outputFcn）

haveOutputFcn=false;

haveOutputFcn=true;

outputs=odeget（options,'

OutputSel'

1:

neq,'

ifisa（outputFcn,'

）

%WithMATLAB6syntaxpassadditionalinputargumentstooutputFcn.

outputArgs=varargin;

refine=max（1,odeget（options,'

Refine'

4,'

））;

ifntspan>

outputAt='

RequestedPoints'

%outputonlyattspanpoints

elseifrefine<

=1

SolverSteps'

%computedpoints,norefinement

RefinedSteps'

%computedpoints,withrefinement

S=（1:

refine-1）/refine;

printstats=strcmp（odeget（options,'

Stats'

'

off'

）,'

%Handletheeventfunction

[haveEventFcn,eventFcn,eventArgs,valt,teout,yeout,ieout]=...

odeevents（FcnHandlesUsed,odeFcn,t0,y0,options,varargin）;

%Handlethemassmatrix

[Mtype,M,Mfun]=odemass（FcnHandlesUsed,odeFcn,t0,y0,options,varargin）;

ifMtype>

0%non-trivialmassmatrix

Msingular=odeget（options,'

MassSingular'

no'

ifstrcmp（Msingular,'

maybe'

）

warning（'

MassSingularAssumedNo'

['

ODE45assumes'

...

MassSingularis'

'

.SeeODE15SorODE23T.'

]）;

elseifstrcmp（Msingular,'

yes'

MassSingularYes'

['

MassSingularcannotbe'

forthissolver.SeeODE15S'

...

orODE23T.'

%IncorporatethemassmatrixintoodeFcnandodeArgs.

[odeFcn,odeArgs]=odemassexplicit（FcnHandlesUsed,Mtype,odeFcn,odeArgs,Mfun,M）;

f0