Using ODE45

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1、BucknellUniversityUsingODE45MATLABHelpMATLAB'sstandardsolverforordinarydifferentialequations(ODEs)isthefunctionode45.ThisfunctionimplementsaRunge-Kuttamethodwithavariabletimestepforefficientcomputation.ode45iddesignedtohandlethefollowinggeneralproblemdy==fy(,)tty()y[

2、1]oodtwheretistheindependentvariable(time,position,volume)andyisavectorofdependentvariables(temperature,position,concentrations)tobefound.Themathematicalproblemisspecifiedwhenthevectoroffunctionsontheright-handsideofEq.[1],fy(,)t,issetandtheinitialconditions,y=yoatti

3、meto,arespecified.ThenoteshereapplytoversionsofMATLABabove5.0andcoverthebasicsofusingthefunctionode45.FormoreinformationonthisandotherODEsolversinMATLAB,seetheon-linehelp.Contents:Syntaxforode45.........................................................................

4、..............................................2Integratingasingle,first-orderequation......................................................................................3Gettingthesolutionatparticularvaluesoftheindependentvariable...................................

5、........4Integratingasetofcoupledfirst-orderequations.........................................................................4Integratingasecond-orderinitial-valueproblem(IVP)................................................................7IntegratinganNth-orderinit

6、ial-valueproblem............................................................................8Changingmodelparameters........................................................................................................9Integratingasecond-orderboundary-valueproblem(

7、BVP)........................................................11Settingoptionsinode45..........................................................................................................12Goingbeyondode45............................................................

8、.....................................................13ENGR210UsingODE451Syntaxforode45ode45maybeinvokedfromthecommandlinevia[t,y]=