1. SCIENTIFIC DISCOVERY THEORY SCIENTIFIC COMPUTING EXPERIMENT

2. EXPERIMENTAL DATA MATHEMATICAL MODEL DISCRETE MODEL COMPUTER MODEL (ALGORITHM) SOLUTION

3. 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

4. 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

5. 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

6. 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