Compuational-Physics
In this repository, you can find various numerical algorithms and their application in solving Physics related equations
Root finding Algorithms:
- I discuss few root finding algorithms - Newton Raphson, Bisection Program and Secant.
- Solved the Schrodinger Equation for a finite well problem using a hybrid root finding algorithm - obtained odd parity and even parity solutions. Theory for the same is available in Griffith's.
Differential Equations (ODE's):
- Analysed Euler's method and Runge Kutta methods for solving an ordinary differential Equation - effect of varying the step size and differential functions on the error.
- Applied the above methods to numerically solve for the Simple Harmonic Oscillations.
Partial Differential Equations:
Solved the heat/diffusion PDE using analytical methods:-
- Explicit Forward Euler method
- Implicit Backward Euler method and
- Crank Nicolson method.
Although I have solved for dirichlet boundary conditions, the code can be easily tweaked for neumann boundary conditions.
Monte carlo methods :
- Solved an integral (1/1+x^2) in the range [0,1] with and without a weight function using monte carlo methods.