Partial differential equations

January 27, 2021 — July 23, 2022

functional analysis
linear algebra


1 Classic PDE systems

Andrew Gibiansky, Fluid Dynamics: The Navier-Stokes Equations is a great and compact introduction.

2 Green’s functions

Figure 1

Cole’s list of Green’s Functions.

TBD. Operator adjoints.

3 Basis function methods

Figure 2

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.
Le Gall. 1999. Spatial Branching Processes, Random Snakes and Partial Differential Equations.
Reid. 2015. Advanced Analytic 18.305 Methods in Science and Engineering.