# Spectral methods in python

I have re-written the codes given in Trefethenâ€™s Spectral Methods in Matlab using python. You can find them in the following links as jupyter notebooks.

If you have any suggestions to improve them or find a mistake, then I would like to hear.

A similar project is another-chebpy. Some of the following code is borrowed from another-chebpy. To get all the files, do

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

You can also read the code on github.

- Convergence of fourth order finite differences
- Convergence of periodic spectral method
- Band-limited interpolation
- Periodic spectral differentiation
- Repetition of Program 4 via FFT
- Variable coefficient wave equation
- Accuracy of periodic spectral differentiation
- Eigenvalues of harmonic oscillator
- Polynomial interpolation in equispaced and chebyshev points
- Polynomials and corresponding equipotential curves
- Chebyshev differentiation of a smooth function
- Accuracy of Chebyshev spectral differentiation
- Solve linear BVP
- Solve nonlinear BVP
- Solve eigenvalue BVP
- Poisson equation on [-1,1]x[-1,1] with u=0 on boundary
- Helmholtz equation
- Chebyshev differentiation via FFT
- Second order Wave Equation on Chebyshev Grid
- Second order Wave Equation using FFT
- Eigenvalues of Mathieu operator
- 5'th eigenvector of Airy equation
- Eigenvalues of perturbed Laplacian
- Pseudospectra of Davies complex harmonic oscillator
- Stability regions for ODE formulas
- Eigenvalues of 2nd-order Chebyshev diff. matrix
- Solve KdV equation, with animation
- Linear BVP with non-homogeneous bc
- Linear BVP with Neumann bc