Here we present some useful numerical methods applied to simple problems, which are a starting point before we work with physics problems, where they are often used. We present the codes in Fortran 90 and Python 3 versions.
| Folder | Content | Programming Language |
|---|---|---|
| Bisection | Bisection method to find a root of a function within an interval | Fortran 90 and Python 3 |
| CG | Conjugate gradient (CG) method to solve a linear matrix system | Fortran 90 and Python 3 |
| LU_scheme | Lower-Upper (LU) scheme to solve a linear matrix system, where the matrix is tridiagonal | Fortran 90 and Python 3 |
| Newton | Newton method to find a root of a function | Fortran 90 and Python 3 |
| SOR | Sucessive-Over relaxation (SOR) scheme to solve a linear matrix system | Fortran 90 and Python 3 |
| Trapezium_rule | Trapezium rule to perform the integration of a function in a given interval | Fortran 90 and Python 3 |
| Simpson_rule | Simpson's rule to perform the integration of a function in a given interval | Fortran 90 and Python 3 |
| Euler | Euler's method to solve ordinary differential equations (ODE) | Fortran 90 and Python 3 |
| RK4 | 4th order Runge-Kutta (RK4) method to solve ordinary differential equations (ODE) | Fortran 90 and Python 3 |
| RKF45 | 4th-5th order Runge-Kutta-Fehlberg (RKF45) method to solve ordinary differential equations (ODE) with adaptative steps | Fortran 90 |
| Shooting | Shooting method to solve ordinary differential equations (ODE) using the Euler method to evolve equations | Fortran 90 |
| Combinatorial | Factorial and combination functions | Fortran 90 |