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


References: (1) Finite Difference Method for Ordinary and Partial Differential Equations, Steady-State and Time-Dependent 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 Differential-Algebraic Equations by Uri M. Ascher and Linda R. Petzold, SIAM, 1998

bulletTentative Schedule: updated regularly


Tuesday: MBI Lecture Hall Thursday: MBI Lecture Hall
Jan 5

Overview of Numerical Methods for PDEs,

Method of lines (MOL) for time-dependent PDEs,

Ref: (1) Chapter 9.2 (p.184)

ODE: explicit, accuracy, stability, convergene

Runge-Kutta, RK45, SSP RK

Ref: (2) & (7) Chapter 1-5


Jan 7

ODE: implicit scheme, consistency, stability, convergence, ode15s

Ref: (2) & (7) Chapter 1-5


Jan 12

Parabolic equation: diffusion, accuracy, stability

Ref: (1) Chapter 9 and (3) Chapter 2-3

Jan 14

Parabolic equation: diffusion-reaction

Ref: (1) Chapter 9 and (3) Chapter 2-3

Jan 19

parabolic equation: stiffness

Ref: (1) Chapter 9 and (3) Chapter 2-3


Jan 21

elliptic equation, finite difference, linear, nonlinear, iterative scheme

Ref: (3) Chapter 5 and (4) Chapter 10-12

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 1-6

Feb 4

hyperbolic equation, numerical methods

Ref: (5) cahpter 1-6

Feb 9

hyperbolic equation, ENO, WENO, and DG

Ref: (5) Chapter 10-18

Feb 11

introduction to free interface problems and numerical techniques

mapping methods in 1D and 2D (conformal mapping)

Feb 16

guest lecture: Monte-Carlo methods

Feb 18

guest lecture: SODEs

Feb 22

MBI workshop

Feb 24

MBI workshop

Mar 2

Level Set Method

Ref: (6) Chapter 1-8

Mar 4

Level Set Method

Mar 9

IMA conference

Mar 11

IMA conference

Mar 15

MBI workshop

Mar 17

MBI workshop