Introduction to pseudospectral methods [1/8], introduction

An introduction to pseudospectral methods Link to presentation: https://ignite.byu.edu/spectral_presentation Link to notes: https://ignite.byu.edu/spectral Link to Github (notes and presentation): https://github.com/byu-books/spectral Part 1/8 Introduction: https://youtu.be/1he8mJGpMTk Part 2/8: Fourier modes: https://youtu.be/QLdW6Ci_DQY Part 3/8: DFT/IDFT: https://youtu.be/YYHFr1_x4ho Part 4/8: 2D DFT/IDFT: https://youtu.be/eA8iUQ-mXxo Part 5/8: Chebyshev polynomials: https://youtu.be/XgkK9imaW78 Part 6/8: Chebyshev interpolation: https://youtu.be/1c2ksXgAKpg Part 7/8: Chebyshev derivatives, examples: https://youtu.be/VzhYhR3sHYI Part 8/8: 2D Chebyshev, notes: https://youtu.be/9DkLiESXPvg Spectral methods can be hard to learn. These videos present an introduction to the derivation and application of the methods for both Fourier and Chebyshev basis functions applicable to periodic and nonperiodic boundary conditions (including Dirichlet, Neumann, and Robin conditions). The focus is on the solution of PDEs, especially parabolic PDEs with time variations for which the method of lines is applied. Examples in one and two dimensions are given. References: Boyd, "Chebyshev and Fourier Spectral Methods" 2nd edition, Trefethen, "Spectral Methods in Matlab"