前森兰变频器的用户朋友您好!言.ppt

《前森兰变频器的用户朋友您好!言.ppt》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、OrdinaryDifferentialEquationsEquationswhicharecomposedofanunknownfunctionanditsderivativesarecalleddifferentialequations.Differentialequationsplayafundamentalroleinengineeringbecausemanyphysicalphenomenaarebestformulatedmathematicallyintermsoftheirrateofchange.v-dependentvariablet-independentvaria

2、ble1Whenafunctioninvolvesonedependentvariable,theequationiscalledanordinarydifferentialequation(orODE).Apartialdifferentialequation(orPDE)involvestwoormoreindependentvariables.Differentialequationsarealsoclassifiedastotheirorder.Afirstorderequationincludesafirstderivativeasitshighestderivative.Ase

3、condorderequationincludesasecondderivative.Higherorderequationscanbereducedtoasystemoffirstorderequations,byredefiningavariable.byLaleYurttas,TexasA&MUniversity2Part7ODEsandEngineeringPracticeFigurePT7.1byLaleYurttas,TexasA&MUniversity3Part7FigurePT7.2byLaleYurttas,TexasA&MUniversity4Chapter25Rung

4、a-KuttaMethodsChapter25ThischapterisdevotedtosolvingordinarydifferentialequationsoftheformEuler’sMethodbyLaleYurttas,TexasA&MUniversity5Chapter25Figure25.2byLaleYurttas,TexasA&MUniversity6Chapter25Thefirstderivativeprovidesadirectestimateoftheslopeatxiwheref(xi,yi)isthedifferentialequationevaluate

5、datxiandyi.Thisestimatecanbesubstitutedintotheequation:Anewvalueofyispredictedusingtheslopetoextrapolatelinearlyoverthestepsizeh.byLaleYurttas,TexasA&MUniversity7Chapter25NotgoodbyLaleYurttas,TexasA&MUniversity8Chapter25ErrorAnalysisforEuler’sMethod/NumericalsolutionsofODEsinvolvestwotypesoferror:

6、TruncationerrorLocaltruncationerrorPropagatedtruncationerrorThesumofthetwoisthetotalorglobaltruncationerrorRound-offerrorsbyLaleYurttas,TexasA&MUniversity9Chapter25TheTaylorseriesprovidesameansofquantifyingtheerrorinEuler’smethod.However;TheTaylorseriesprovidesonlyanestimateofthelocaltruncationerr

7、or-thatis,theerrorcreatedduringasinglestepofthemethod.Inactualproblems,thefunctionsaremorecomplicatedthansimplepolynomials.Consequently,thederivativesneededtoevaluatetheTaylorseriesexpansionwouldnotalwaysbeeasyto