Computational-PDEs

Lecture notes for Computational methods for PDEs at University of Leicester, 2023

Chapter 0: Welcome to Computational Methods for PDEs html pdf

Chapter 1: From finite differences to a spectral method for periodic functions html pdf notebook

Chapter 2: Fourier methods for periodic functions html pdf notebook

Chapter 3: Chebyshev methods for non-periodic functions html pdf notebook

Chapter 4: orthogonal polynomial methods for differential equations html pdf notebook

Chapter 5: Consistency, stability and convergence of methods for evolutionary PDEs html pdf notebook

Sources

1. A Practical Guide to Pseudospectral Methods (1998), B. Fornberg
2. Computational Methods for Partial Differential Equations (2009), M. Georgoulis
3. A First Course in the Numerical Analysis of Differential Equations (2009), A. Iserles
4. Fast algorithms using orthogonal polynomials (2020), S. Olver, R.M. Slevinsky and A. Townsend. Acta Numerica, 29, pp.573-699.
5. Sheehan Olver's Numerical Analysis notes (2022)
6. Applied Complex Analysis notes (2021)
7. Christoph Ortner's notes on Numerical Methods for Differential Equations (2022)
8. Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations (1996), L.N. Trefethen
9. Spectral Methods in Matlab (2000), L.N. Trefethen
10. Approximation Theory and Approximation Practice (2019), L.N. Trefethen
11. A MATLAB differentiation matrix suite (2000), J.A.C. Weideman and S.C. Reddy, ACM Transactions on Mathematical Software (TOMS), 26(4), pp.465-519.