Cours : METHODES NUMERIQUES

Aperçu des sections

At the end of this course, students should be able to:

Familiarize with numerical methods and their applications in mathematical computations.

Chapter 1: Solving Non-linear Equations f(x)=0 (3 weeks)

Introduction to calculation errors and approximations.

Introduction to methods for solving non-linear equations.

Bisection method.

Successive approximations method (Fixed point).

Newton-Raphson method.

Chapter 2: Polynomial Interpolation (2 weeks)

General introduction.

Lagrange polynomial.

Newton polynomial.

Chapter 3: Function Approximation (2 weeks)

Quadratic approximation and mean method.

Orthogonal or pseudo-orthogonal systems. Approximation by orthogonal polynomials.

Trigonometric approximation.

Chapter 4: Numerical Integration (2 weeks)

General introduction.

Trapezoidal rule.

Simpson's rule.

Quadrature formulas.

Chapter 5: Solving Ordinary Differential Equations (Initial Value or Cauchy Problem) (2 weeks)

General introduction.

Euler's method.

Improved Euler's method.

Runge-Kutta method.

Chapter 6: Direct Methods for Solving Linear Equation Systems (2 weeks)

Introduction and definitions.

Gauss method and pivoting.

LU factorization method.

Cholesky factorization method.

Thomas Algorithm (TDMA) for tridiagonal systems.

Chapter 7: Iterative Methods for Solving Linear Equation Systems (2 weeks)

Introduction and definitions.

Jacobi method.

Gauss-Seidel method.