Numerical Methods II, Spring 2012

Course home page

Details and Weekly schedule

Resources

Assignments

Lecture notes

• Week 1
• Week 2, Reference on error expansions and extrapolation
• Week 3, Rough notes on convergence for ODE
• Week 3, Rough notes on linear multistep methods. The book probably is better.
• Week 3, Rough notes on implicit methods. The book probably is better.
• Week 4, Rough notes on discretization of the Laplace equation.
• Week 5, Rough notes on the discrete Fourier transform and its theoretical applications
• Week 6, Time dependent PDE, difference approximations, stability via Fourier analysis

Reference books

• Arieh Iserles, A First Course in the Numerical Analysis of Differential Equations
  • Required text for the class.
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• Germund Dahlquist and Åke Björk, Numerical Methods
  • Simplest the best book on numerical analysis ever written. The Dover edition is very cheap. It has a great discussion of linear multistep methods and asymptotic error expansions. Some of the material is dated, but all of it is interesting.
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• Robert Richtmeyer and K.W. Morton, Difference Methods for Initial Value Problems
  • Old but great reference for some of the deep theoretical parts of PDE solving. Good discussion of stability theory, particularly von Neumann analysis. Very careful attention to detail in delicate cases with multiple eigenvalues in amplification matrices. The Kreiss matrix theorem.
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• Yousef Saad, Iterative Methods for Sparse Linear Systems
  • Linear algebra for solving PDE problems. A good reference for GMRES, which is not covered in the Iserles text. Lots of stuff about sparse matrices, which the class will not cover. Mostly from a linear algebra rather than an analysis point of view, which leaves out lots of information you have about real numerical PDE problems. You can get it from SIAM or download the .pdf file (using google or clicking on the link in the title above.
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• Anne Greenbaum, Iterative Methods for Solving Linear Systems
  • As the title says. Another good source for GMRES and other iterative methods.
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