# Numerical Analysis Aug-Dec 2013

For latest and updated codes, see https://github.com/cpraveen/na

## Students

- Abhrojyoti Sen
- Amrita Ghosh
- Aniket Bhanja
- Arka Mallick
- Arnab Roy
- Arunima Bhattacharya
- Debabrata De
- Debdeep Bhattacharya
- Manish Kumar Singh
- Manmohan

## Reference texts

- K. Atkinson, Introduction to Numerical Analysis, Wiley
- David Kincaid and E. Ward Cheney, Numerical Analysis: Mathematics of scientific computing

## Computer programs

Codes are available here

https://github.com/cpraveen/na2013

You can also get them using git

```
git clone https://github.com/cpraveen/na2013
```

### Computer arithmetic

- Store 1/10 and print it to see the conversion of real number to floating number
- Demonstration of unit round
- Example of overflow error and how to avoid it
- Errors due to subtracting nearly equal quantities
- Sensitivity of polynomial roots
- Unstable iterations
- Unstable iterations: ODE example

### Root finding

- Bisection method: matlab, python
- Newton method: matlab, python

### Interpolation

- Condition of vandermonde matrix: matlab
- Interoplate nice function like cos(x) on uniform data: matlab
- Interpolate on uniform and chebyshev points, Runge phenomenon: matlab
- Interpolate abs(x) on uniform and chebyshev points: matlab
- Interpolation to show Runge phenomenon, barycentric lagrange formula: python
- Behaviour of interpolation error on uniform and chebyshev points: matlab
- Behaviour of newton forward differences under roundoff error: matlab
- Adaptive piecewise P1 interpolation: matlab
- Trigonometric interpolation of periodic function: matlab
- Comparison of trigonometric and polynomial interpolation: matlab
- Convergence of trigonometric interpolation: matlab

### Solving ODE

- Euler method, convergence test: python
- Euler method, convergence test: python
- Euler method, instability example: python
- Trapezoidal method, convergence test: python
- Absolute stability domains of AB, AM, BDF schemes: python
- Example of stiff ODE: python
- ODE with periodic solution, quadratic invariant: python