Here you can find some implementations of various numerical methods, in C++ and MATLAB. Α coherent format is preserved, in order to perform some basic comparison between the methods.
- Picard method [x=g(x)]
- Newton-Raphson method
- Newton method for simultaneous equations
- Picard method for simultaneous equations
- Gauss-Seidel method
- Power method
- Simpson method (numerical integration)
- Runge-Kutta method - 2nd & 4th order (ODE evaluation)
- Runge-Kutta method - Stability study
- Shooting method with Runge-Kutta method (Boundary conditions problems)
- Liebmann method (2nd order Elliptic PDEs -- Poisson's function) + SOR scheme
- Lax-Wendroff method (2nd order Hyperbolic PDEs -- Wave function)
If a method performs calculations on a grid, MATLAB is used for matrix computations.
More specifically, these are some exercises submitted for the elective course Numerical Analysis by prof. Nikolaos Stergioulas, at the Physics department of Aristotle University of Thessaloniki.
For more information you can refer to Numerical_Methods_report.pdf.
(C) 2019, Athanasios Mattas
[email protected]