Partial differential equations
January 27, 2021 — July 23, 2022
Placeholder.
1 Classic PDE systems
Andrew Gibiansky, Fluid Dynamics: The Navier-Stokes Equations is a great and compact introduction.
2 Green’s functions
Cole’s list of Green’s Functions.
TBD. Operator adjoints.
3 Basis function methods
4 Laplacian methods
5 Eulerian methods
6 for fluids specifically
See CFD.
7 References
Bluman. 1983. “On Mapping Linear Partial Differential Equations to Constant Coefficient Equations.” SIAM Journal on Applied Mathematics.
Borthwick. 2016. Introduction to Partial Differential Equations. Universitext.
Borzì, and Schulz. 2012. Computational Optimization of Systems Governed by Partial Differential Equations. Computational Science and Engineering Series.
Brezis. 2010. Functional Analysis, Sobolev Spaces and Partial Differential Equations.
Dynkin. 2004. Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations. University Lecture Series, v. 34.
Evans. 1998. Partial Differential Equations.
Kovacic. 1986. “An Algorithm for Solving Second Order Linear Homogeneous Differential Equations.” Journal of Symbolic Computation.
Kuzmin. 2010. A Guide to Numerical Methods for Transport Equations.
Reid. 2015. Advanced Analytic 18.305 Methods in Science and Engineering.