1. Modelling and scientific programming

2. Objectives To learn to develop computer programs that are  Correct  Efficient  Adaptable  Portable

3. Remarks Price of computers  Cost of programming development  Clear programmes  time for development   costs  No unique solution  choose most appropriate solution

4. Content Course : 10h Introduction Errors and numerical stability Numerical analysis Linux Fortran 90 C++ Practical tutorials (20 hours) Project

5. Chapter 1 : Introduction Scientific research traditionally involves 2 main activities Experiments Modelling Observations Theories Predictions Suggest theories Test theories Interpret experiments Suggest theories confrontations

6. Classical mechanics ≡ Celestial mechanics  Horoscopes   observe sky  collect data  contradict Ptolemy’s geocentric model  introduce heliocentric model 85 – 165 AD Classical mechanics

7.  Nicolaus Copernicus heliocentric model circular trajectories 1473-1453

8. Develop observational tools and methods  Tycho Brahe 1546-1601 Collect accurate data

9.  Johannes Kepler  Fit curves to data 1571-1630  3 laws Elliptical orbit for Mars

10.  Galileo Galilei modern scientific method  Observe : pendulum  Experiment : inclined plane free fall from the Tower of Pisa  Model Technical progress : optics  telescope  jump in the quality of observations 1564-1642

11.  Isaac Newton Develop mathematical tools (calculus) Unify apparently disconnected facts movements of planets movement of the Moon falling bodies  3 fundamental laws of classical mechanics  law of gravitation 1643-1727

12. Since Newton … Test theory  predict comets, new planets, … Improve methods  Corrections : 3-body problem, rigid body, tidal forces, precession, nutation, …  New technologies  accurate measurements  Many-body problems : Euler, Lagrange, Laplace, Gauss, …  complex methods to approximate motions of bodies = celestial mechanics  Transformation and integration of equations of motions = analytic mechanics Improve theory  Special relativity  General relativity Halley

16. Numerical approach = third approach, complementary to the 2 others Experiments ModellingNumerical simulation Suggest model Generate data Suggest theories Test theories Interpret experiments Suggest experiments Model real processes Suggest experiments Analyse data Provide equations Interpret results Suggest theories Allow accurate calculations large calculations

17. Advantages of numerical simulation Relatively easy to implement Economical Efficient Quantitative Applicable to complex systems Allow numerical experimentation Allow systematic investigation (scaling laws) Applicable to apparently very different systems, described by similar equations