The ipython notebooks in these lectures cover basic aspects of solving partial differential equations using local and global collocation. Included in this family of methods are standard finite differences, spectral methods using Chebyshev, Hermite, Laguerre, Fourier and Sinc basis functions, and multidimensional finite difference methods with isotropic error.
- Introduction
- Differentiation matrices, Spectral accuracy
- Polynomial differentiation matrices
- Bounded spaces : Chebyshev differentiation matrices
- Semi-bounded spaces : Hermite differentiation matrices
- Unbounded spaces : Laguerre differentiation matrices
- Periodic spaces : Fourier and Sinc differentiation matrices
- Time-independent boundary value problems
- Time-dependent boundary value problems
- Eigenvalue problems
- Integrals and quadrature formulae
- Boundary conditions
- Beyond collocation