Numerical Methods for Partial Differential Equations

Calendar

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