Numerical Methods 390-FS1-3MNU

Numerical calculus: root finding (secant method, bisection, Newton-Raphson method), numerical integration (Newton-Cotes formulas, Gaussian quadratures), minimization of functions (conjugate directions method, conjugate gradient method, annealing method), integration of ordinary differential equations (Euler method, multistep and implicit methods, leapfrog method, Runge-Kutta method, stability and acuracy of difference schemes), partial differential equations (elliptic equations – relaxation method, hyperbolic equations – Lax scheme, parabolic equations – Crank-Nicholson scheme, stability analysis), integral equations.

Numerical algebra: solving set of linear equations (Gauss-Jordan elimination, LU decomposition (Crout method), iterative methods), nonlinear set of equations (iterative methods), eigenvalues and eigenvectors (Jacobi method for a symmetric matrix).

Numerical probability: uniformly distributed pseudo-random numbers, Monte Carlo quadrature, pseudo-random number generators for any distribution (von Neumann and Metropolis algorithms), Monte Carlo method.

Fast Fourier Transform: differentiating, integrating (convolution, correlation), and solving partial differential equations (split operator method).