numalg 1.0.6

Numerical analysis algorithms

1. Error theory: floating point systems, relative and absolute errors, significant digits, conditioning and stability.

2. Nonlinear equations: Fixed point, Newton-Raphson, Secant and bisection.

3. Nonlinear systems: Generalized Newton method.

4. Linear systems: Jacobi, Gauss-Seidel and SOR methods.

5. Function approximation: Polynomial interpolation (Newton and Lagrange). Linear and cubic splines. Least squares method.

6. Numerical integration: Mid point, Trapezoidal, Simpson and Gauss-Legendre with two and three nodes.

7. Ordinary differential equations (one equation or a system of equations): Euler, Taylor of order 2. Implicit Euler method. Runge-Kutta methods of order 2 (Heun and Midpoint), and Runge-Kutta of order 4.

8. Boundary value problems: finite difference method.

© Isabel Reis dos Santos, IST Ulisboa, 2024