This repository contains the programming assignments completed in the course PHY F313 Computational Physics in Semester 1 2020 - 2021. The course serves as an introduction to numerical methods used in mathematics and physics.
All programming assignments have been implemented using the MATLAB programming language (Version: R2018b)
The bisection method is a root-finding method that applies to any continuous function for which one knows two function values with opposite signs.
The Newton-Raphson method is a root-finding algorithm that successively produces approximations to roots of a real-valued function using an initial guess and the function's derivative.
-
Applications of Newton-Raphson Method
Particle in a finite potential well
Gaussian elimination is an algorithm in for solving a system of linear equations. It involves a sequence of operations performed on the corresponding matrix of coefficients for the system.
The Jacobi method is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until the method converges.
-
Kirchoff current equations for an electrical circuit.
The power method is an eigenvalue algorithm: given a diagonalizable matrix A, the algorithm outputs the largest absolute eigenvalue of A, and its corresponding eigenvector.
-
Applications of Power Method
- Runge-Kutta Methods
The Runge–Kutta methods are a family of implicit and explicit iterative methods used in temporal discretization for the approximate solutions of ordinary differential equations.