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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

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