 
 Course:Numerical methods for partial differential equations and their applications in biology. 

References:
(1) Finite Difference Method for Ordinary and Partial Differential Equations, SteadyState and TimeDependent Problem by Randall J. LeVeque, SIAM, 2007
(2) A first Course in the Numerical Analysis of Differential Equations by Arieh Iserles, Cambridge Textx in Applied mathematics, 1996
(3) Numerical Solution of Partial Differential equations, Finite Difference Methods, by G. D. Smith, third edition, Oxford Applied Mathematics and Computing Science Series, 1985
(4) Understanding and Implementing the Finite Element Method, by Mark S. Gockenbach, SIAM, 2006
(5) Numerical Methods for Conservation Laws by Randall J. LeVeque, Birkhauser, 1992
(6) Level set methods and dynamic implicit surfaces by Stanley Osher and Ronald P. Fedkiw, Springer, 2003
(7) Computer Methods for Ordinary Differential Equations and DifferentialAlgebraic Equations by Uri M. Ascher and Linda R. Petzold, SIAM, 1998

 Tentative Schedule: updated regularly 
Tuesday: MBI Lecture Hall 
Thursday: MBI Lecture Hall 
Jan 5
Overview of Numerical Methods for PDEs,
Method of lines (MOL) for timedependent PDEs,
Ref: (1) Chapter 9.2 (p.184)
ODE: explicit, accuracy, stability, convergene
RungeKutta, RK45, SSP RK
Ref: (2) & (7) Chapter 15

Jan 7
ODE: implicit scheme, consistency, stability, convergence, ode15s
Ref: (2) & (7) Chapter 15

Jan 12
Parabolic equation: diffusion, accuracy, stability
Ref: (1) Chapter 9 and (3) Chapter 23

Jan 14
Parabolic equation: diffusionreaction
Ref: (1) Chapter 9 and (3) Chapter 23

Jan 19
parabolic equation: stiffness
Ref: (1) Chapter 9 and (3) Chapter 23

Jan 21
elliptic equation, finite difference, linear, nonlinear, iterative scheme
Ref: (3) Chapter 5 and (4) Chapter 1012

Jan 26
elliptic equation, multigrid
Ref: (3) Chapter 13

Jan 28
elliptic & parabolic equation, finite element, (matlab, comsol)
Ref: (3) Chapter 5 and(4) Chapter 4

Feb 2
hyperbolic equation, theory
Ref: (5) cahpter 16

Feb 4
hyperbolic equation, numerical methods
Ref: (5) cahpter 16

Feb 9
hyperbolic equation, ENO, WENO, and DG
Ref: (5) Chapter 1018

Feb 11
introduction to free interface problems and numerical techniques
mapping methods in 1D and 2D (conformal mapping)

Feb 16
guest lecture: MonteCarlo methods

Feb 18
guest lecture: SODEs

Feb 22
MBI workshop

Feb 24
MBI workshop

Mar 2
Level Set Method
Ref: (6) Chapter 18

Mar 4
Level Set Method

Mar 9
IMA conference

Mar 11
IMA conference

Mar 15
MBI workshop

Mar 17
MBI workshop


