This repository archives the code used for MATH6008 Numerical PDEs.
Theory of PDE, Finite Difference & Finite Element:
- Allaire G (2007) Numerical Analysis And Optimization: An introduction to mathematical modelling and numerical simulation, Oxford University Press. Chp 1-6.
Finite Volume Method:
- Versteeg HK, Malalasekera W (2007) An introduction to computational fluid dynamics: the finite volume method, Harlow, Essex, England, Longman Scientific & Technical, New York : Wiley. Chp 4, 5, 11.
Machine Learning for PDEs:
- E W, Yu B (2018) The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems. Commun Math Stat 6: 1–12.
- Raissi M, Perdikaris P, Karniadakis GE (2019) Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378: 686–707.
- Bishop CM, Bishop H (2024) Deep Learning: Foundations and Concepts, Cham, Springer International Publishing.
Spectral Method:
- Kopriva DA (2009) Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers, Dordrecht, Springer Netherlands. Chp 1-4.
A tutorial of how to install Jupyter notebook can be found in this link.