/Compuational-Physics

Numerical algorithms applied to problems of Physics

Primary LanguageJupyter Notebook

Compuational-Physics

In this repository, you can find various numerical algorithms and their application in solving Physics related equations

Root finding Algorithms:

  1. I discuss few root finding algorithms - Newton Raphson, Bisection Program and Secant.
  2. 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):

  1. 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.
  2. Applied the above methods to numerically solve for the Simple Harmonic Oscillations.

Partial Differential Equations:

Solved the heat/diffusion PDE using analytical methods:-

  1. Explicit Forward Euler method
  2. Implicit Backward Euler method and
  3. Crank Nicolson method.

Although I have solved for dirichlet boundary conditions, the code can be easily tweaked for neumann boundary conditions.

Monte carlo methods :

  1. Solved an integral (1/1+x^2) in the range [0,1] with and without a weight function using monte carlo methods.