Initial value problems

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1、NumericalMethodsinChemicalEngineering6Initialvalueproblems6Initialvalueproblems....................................................................................16.1Overview..................................................................................................26.2Euler'smethod.......

2、...................................................................................36.2.1Testproblem-afirstorderreactioninabatchreactor....................56.2.2PerformanceoftheEulermethod.....................................................66.2.3AccuracyoftheEulerscheme..........................

3、................................96.2.4StabilityoftheEuler-scheme..........................................................106.2.5Amorerigorousstabilityanderroranalysis...................................116.2.6Extendingtheerrorandstabilityanalysistonon-linearODEs......136.3TheImplicitEulermethod..

4、...................................................................146.3.1StabilityoftheImplicitEulerscheme.............................................176.4SystemsofODEs...................................................................................196.4.1UsingtheImplicitEulermethodforsystems

5、ofODEs..................216.5StabilityofnumericalsolutionswhensolvingmanyODEs..................256.5.1InherentstabilityofsystemsofseverallinearODEs......................256.5.2Thestabilityofnumericalsolutionstolinearsystems....................286.5.3Extendingthestabilityanalysistonon-linearsystem

6、s...................316.6Stiffsystemsandthechoiceoftimestep...............................................326.7Higherorderintegrationmethods..........................................................3326.7.1O(dt)time-steppingscheme...........................................................3446.7.2

7、O(dt)time-steppingscheme...........................................................386.8Conclusions............................................................................................41-1-NumericalMethodsinChem