Semester 2
Teaching Unit : UEM 1.2
Subject 3: Applied Numerical Methods
VHS: 45h00 (Lectures: 1h30, Tutorials: 1h30)
Credits: 3
Coefficient: 1
1- Teaching Objectives
The main goal of teaching this module is to build a robust foundation for the first-year master's student in production to solve the different types of differential equations that govern hydrocarbon production phenomena using numerical methods and programming tools such as MATLAB.
2-Recommended prior knowledge
Skills acquired during his bachelor's degree training in production 1 and 2; the modules: Mathematics and computer science.
3-Content of the material
Chapter I : Analytical solution of ordinary differential equations.
II.1 First-order linear differential equation.
II.2 Second order linear differential equation.
Chapter II Numerical solution of ordinary differential equations of order 1 (initial condition or Cauchy problem).
III.1 Cauchy's Problem
III.2 Euler's Method
III.3 Modified Euler Method
III.4 Taylor Method
III.5 Runge-Kutta method of order 2 and order 4
Chapter III: Numerical solution of differential equations of order greater than 1 and system of differential equations (initial condition problem or Cauchy problem) .
IV.1 Cauchy's Problem
IV.2 Euler's Method
IV.3 Modified Euler Method
IV.4 Taylor Method
IV.5 Runge-Kutta method of order 2 and order 4
Chapter IV: Numerical solution of ordinary differential equations of order (2) (Boundary or Dirichlet problem).
V.1. Direchlet problem for ordinary differential equations (2).
V.2 Finite Difference Method
Rayleighritz method
V.4 Firing Method
Chapter V: Optimization Methods
V.1 Generalities on optimization problems
V.2 Optimization in 1 dimension
V.3. Optimization in dimension n>2
4-Evaluation Method
Written assessment (exams) and continuous assessment (presentations, quizzes) .
5-Bibliographical References
1- Jean-Pierre NOUGIER, Numerical Calculation Methods, MASSON, Paris 1991.
2- Kurt ARBENZ and Alfred WOHLHAUSER, Numerical Analysis, O. PU , central square of Ben Aknoun (Algiers).
3- C. Brezinski, Introduction to the practice of numerical calculation, Dunod, Paris 1988.
4 - G. Allaire and SM Kaber , Numerical Linear Algebra, Ellipses, 2002.
5 - M. Crouzeix and A.-L. Mignot, Numerical analysis of differential equations, Masson, 1983.
6- S. Delabrière and M. Postel, Approximation methods. Differential equations. Scilab applications, Ellipses, 2004.
7- PG Ciarlet , Introduction to numerical matrix analysis and optimization , Masson , Paris, 1982.
8 - J.-P. Demailly , Numerical Analysis and Differential Equations. Presses Universitaires de Grenoble, 1996.
9- E. Hairer , SP Norsett and G. Wanner, Solving Ordinary Differential Equations, Springer, 1993.
10 - G. Christol, A. Cot and C.-M. Marle, Differential Calculus, Ellipses, 1996.
- Teacher: Mohamed DOUAK