Numerical Methods for Partial Differential Equations

Lecture Notes

LEC #	TOPICS	FILES
1	Fundamental concepts and examples	(PDF)
2	Well-posedness and Fourier methods for linear initial value problems	(PDF)
3	Laplace and Poisson equation	(PDF)
4	Heat equation, transport equation, wave equation	(PDF)
5	General finite difference approach and Poisson equation	(PDF)
6	Elliptic equations and errors, stability, Lax equivalence theorem	(PDF)
7	Spectral methods	(PDF)
8	Fast Fourier transform (guest lecture by Steven Johnson)
9	Spectral methods	(PDF)
10	Elliptic equations and linear systems	(PDF)
11	Efficient methods for sparse linear systems: Multigrid	(PDF)
12	Efficient methods for sparse linear systems: Krylov methods	(PDF)
13	Ordinary differential equations	(PDF)
14	Stability for ODE and von Neumann stability analysis	(PDF)
15	Advection equation and modified equation	(PDF)
16	Advection equation and ENO/WENO	(PDF)
17	Conservation laws: Theory	(PDF)
18	Conservation laws: Numerical methods	(PDF)
19	Conservation laws: High resolution methods	(PDF)
20	Operator splitting, fractional steps	(PDF)
21	Systems of IVP, wave equation, leapfrog, staggered grids	(PDF)
22	Level set method	(PDF)
23	Navier-Stokes equation: Finite difference methods	(PDF)
24	Navier-Stokes equation: Pseudospectral methods	(PDF)
25	Particle methods	(PDF)
26	Project presentations