Numerical Methods

The course revolved around using various computational methods to arrive at an approximate solution for a given equation.

We first discuss solving simple equations using the following methods:

1. Iterative methods like Bisection, Fixed point and Newton-Raphson to find the roots of an equation
2. Interpolation methods like Lagrange interpolation, Newton's forward and backward difference method
3. Numerical integration methods like Rectangular rule, Midpoint rule, Trapezoidal rule and Simpson's rule
4. Composite versions of the above integration rules
5. Quadrature formulas like Gaussian quadrature
6. Numerical differentiation methods like forward, backward and central difference formulas

Then we move on to solving Initial Value Problems using the following methods:

1. Euler's method
2. Taylor's method
3. Trapezoidal method
4. Runge Kutta method
5. Adam-Bashforth explicit method
6. Adam-Moulton implicit method
7. Predictor Corrector method

We also solve Boundary Value Problems using the following methods:

1. Linear Shooting method
2. Non Linear Shooting method
3. Finite difference method

Lastly, we solve a system of linear equations using the following methods:

1. Gaussian elimination with backward substitution
2. Gauss Jacobi iterative method
3. Gauss Seidel iterative method

Each problem set above consists a list of questions and python implementations of the methods mentioned to solve them.