SCIENTIFIC DISCOVERY
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SCIENTIFIC DISCOVERY. THEORY. SCIENTIFIC COMPUTING. EXPERIMENT. EXPERIMENTAL DATA. MATHEMATICAL MODEL. DISCRETE MODEL. COMPUTER MODEL (ALGORITHM). SOLUTION. EXPERIMENTAL ERRORS UNCERTAINTIES. EXPERIMENTAL DATA. MATHEMATICAL MODEL. MODELING ERRORS. DISCRETE MODEL.

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SCIENTIFIC DISCOVERY

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Scientific discovery

SCIENTIFIC DISCOVERY

THEORY

SCIENTIFIC COMPUTING

EXPERIMENT


Scientific discovery

EXPERIMENTAL DATA

MATHEMATICAL MODEL

DISCRETE MODEL

COMPUTER MODEL

(ALGORITHM)

SOLUTION


Scientific discovery

EXPERIMENTAL ERRORS

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


Scientific discovery

EXPERIMENTAL ERRORS

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


Scientific discovery

ERROR CONTROL PROCESSES

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

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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