SLN 1198, MWF 12:30-1:20, Loew Hall 101
Approximate and Numerical Analysis III
Randall J. LeVeque
office hours: MW 1:30-3:30
Finite-difference methods for time-dependent differential equations.
Multistep methods, stiff equations, implicit methods.
Hyperbolic and parabolic partial differential equations.
Stability and convergence theory.
AMath 581 or AMATH 584
The main topic is finite difference methods for time-dependent differential
- Review of numerical methods for ODEs (initial value problems)
- Consistency, convergence
- Zero stability and absolute stability, stability regions
- Linear multistep and Runge-Kutta methods
- Stiff problems, BDF methods
- Numerical Methods for time-dependent partial differential equations
- Hyperbolic and parabolic equations
- Explicit and implicit methods
- Lax-Richtmyer stability, von Neumann analysis
- Method of lines approach, relation to stiff ODEs
- Finite volume methods
- Introduction to shock capturing methods, flux limiters
- Spectral and pseudospectral methods
- Convection-diffusion and reaction-diffusion equations
- Course Notes for 585-6 by R.J. LeVeque
- The first installment contains material on methods for ODEs and will be
used during the first two weeks of class:
- Chapters 2--5 were covered in AMath 585. These chapters are available
here if you did not get them last quarter and want to see this
- The second installment of 586 notes, Chapters 9-13:
- The third installment of 586 notes, Chapter 14:
- The fourth installment of 586 notes, Chapter 15-17:
- On reserve in the Engineering Library:
- J. D. Lambert, Numerical methods for ordinary differential systems:
the initial value problem, Wiley, 1991.
- A. Iserles. Numerical Analysis of Differential Equations.
Cambridge University Press, 1996.
- J. C. Strikwerda, Finite difference schemes and partial
differential equations, Wadsworth & Brooks/Cole, 1989.
Follow links in the table below to obtain a copy of the homework in
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||Homework Problem Sets
| Week 1
||M, April 1
||First day of classes
| Week 2
||F, April 12
||Homework 1 due
| Week 5
||M, April 29
||Homework 2 due
| Week 7
||Monday, May 13
||Homework 3 due
| Week 7
||F, May 17
| Week 9
||M, May 27
||W, May 29
||Homework 4 due
| Week 10
||F, June 7
| Finals week
||W, June 12
||Final project due
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