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## PowerPoint Slideshow about 'SCIENTIFIC DISCOVERY' - urian

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Presentation Transcript

UNCERTAINTIES

EXPERIMENTAL DATA

MATHEMATICAL MODEL

MODELING ERRORS

DISCRETE MODEL

DICRETIZATIONERRORS

COMPUTER MODEL

(ALGORITHM)

ROUND-OFF ERRORS

UNCERTAINTIES

+MODELING ERRORS

+DISCRETIZATION ERRORS

+ROUND-OFF ERRORS

SOLUTION

UNCERTAINTIES

Uncertainty Quantification

EXPERIMENTAL DATA

MATHEMATICAL MODEL

MODELING ERRORS

Validation

DISCRETE MODEL

DICRETIZATIONERRORS

Verification

COMPUTER MODEL

(ALGORITHM)

ROUND-OFF ERRORS

Numerical Stability

UNCERTAINTIES

+MODELING ERRORS

+DISCRETIZATION ERRORS

+ROUND-OFF ERRORS

Accuracy

SOLUTION

VALIDATION: Are we solving the correct equation?

--Reduction of modeling errors

VERIFICATION: Are we solving the equation correctly?

--Reduction of discretization errors

UNCERTAINTY QUANTIFICATION: Characterization of uncertainties in problem

---Variability of input and/or model parameters

Example

L : Length of pendulum

m : Mass of pendulum

g : Gravitational acceleration

a : Initial angle

θ

Pendulum

θ’’(t) + m g/L sin(θ(t))=0, t >0,

Θ(0)= a

Θ’(0)=0

Mathematical Model

θ‘’ + m g /L θ =0, t >0

θ(0)=a

θ’(0)=0

Discrete Model, RK Methods

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