Teaching

Numerical methods for the solution of differential equations (AM 213B)

Course Description: This course provides an introduction to numerical methods for solving of ordinary and partial differential equations (ODEs and PDEs). The course focuses on the derivation of discrete solution methods for a variety of differential equations, their stability analysis and convergence. The course also provides hands-on experience on implementing numerical algorithms using MATLAB/Octave programming environments.

Instructor: Prof. Daniele Venturi (venturi AT ucsc.edu) 

COURSE NOTES: 

  • The initial value problem for ODEs (PDF)
  • Overview of numerical methods for ODEs (PDF)
  • Consistency of numerical methods for ODEs (PDF)
  • Zero stability and convergence (PDF)
  • Absolute stability (PDF)
  • Boundary value problems (PDF)
  • Numerical methods for boundary value problems (PDF)
  • Numerical methods for PDEs (PDF)
  • Convergence analysis of finite difference methods for PDEs (PDF)
  • Numerical schemes for conservation laws (PDF)

Recommended Textbooks 

  • J. C. Strikwerda, ``Finite difference schemes and partial differential equations'', SIAM 2004 (book)
  • E. Hairer, S. P. Norsett and G. Wanner, ``Solving ordinary differential equations I: nonstiff problems'', Springer 2008 (book) 
  • A. Quarteroni, F. Salieri, R. Sacco ``Numerical mathematics'', Springer 2007 (book)
  • R. LeVeque, ``Finite difference methods for ordinary and partial differential equations'', accessible online from VPN or campus network: http://epubs.siam.org/doi/book/10.1137/1.9780898717839
  • L. N. Trefethen, ``Finite difference and spectral methods for ordinary and partial differential equations'', available online at http://people.maths.ox.ac.uk/trefethen/pdetext.html 
  • J. Hesthaven, S. Gottlieb and D. Gottlieb, ``Spectral methods for time-dependent problems'', Cambridge, 2006 (book)
  • J. D. Lambert, ``Numerical methods for ordinary differential equations: the initial value problem'', Wiley & Sons, 1991.