MIT流体力学课件3

《MIT流体力学课件3》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、IntroductiontoNumericalAnalysisforEngineers•FundamentalsofDigitalComputing–DigitalComputerModels–Convergence,accuracyandstability–Numberrepresentation–Arithmeticoperations–Recursionalgorithms•ErrorAnalysis–Errorpropagation–numericalstability–Errorestima

2、tion–Errorcancellation–Conditionnumbers2.29NumericalMarineHydrodynamicsLecture3ErrorPropagationSphericalBesselFunctionsDifferentialEquationSolutions2.29NumericalMarineHydrodynamicsLecture3ErrorPropagationSphericalBesselFunctionsForwardRecurrenceForwardR

3、ecurrenceUnstableBackwardRecurrenceMiller’salgorithmStableN~x+202.29NumericalMarineHydrodynamicsLecture3ErrorPropagationEuler’sMethodDifferentialEquationExampleDiscretizationFiniteDifference(forward)RecurrenceCentralFiniteDifferenceeuler.m2.29NumericalM

4、arineHydrodynamicsLecture3ErrorAnalysisNumericalInstabilityExampleEvaluateIntegralBackwardRecurrenceRecurrenceRelationProof3-digitRecurrence>y2!!<0!!CorrectExercise:MakeMATLABscript2.29NumericalMarineHydrodynamicsLecture3ErrorPropagationAbsoluteErrorsΔy

5、~f’(x)ΔxFunctionofonevariableΔx=x-xGeneralErrorPropagationFormulaxx2.29NumericalMarineHydrodynamicsLecture3ErrorPropagationExampleMultiplicationErrorPropagationFormula=>=>=>=>RelativeErrorsAddforMultiplication2.29NumericalMarineHydrodynamicsLecture3Erro

6、rPropagationExpectationofErrorsAdditionTruncationStandardError2ErrorExpectationnRoundingStandardErrorbettermeasureofexpectederrors2.29NumericalMarineHydrodynamicsLecture3ErrorPropagationErrorCancellationFunctionofonevariableMax.errorErrorcancellationSta

7、nd.error2.29NumericalMarineHydrodynamicsLecture3ErrorPropagationConditionNumbery=f(x)xxyyx=x(1+α)y=y(1+β)ProblemConditionNumberProblemill-conditionedErrorcancellationexampleWell-conditionedproblem2.29NumericalMarineHydrodynamicsLecture3ErrorPropagationC

8、onditionNumberProblemConditionNumberKisalgorithconditionnumber,whichAmaybemuchlargerthantheKduePtolimitednumberrepresentation.Solution•Higherprecision•Rewritealgorithm4SignificantDigitsWell-conditionedAlgorithmAlgorithmConditionN