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)

Teaching Assistant: George Labaria (glabaria AT soe.ucsc.edu)

Main Lectures: Tu/Th 9:50-11:25AM,  Earth and Marine Sciences B210

Office Hours: Tuesday 12-1PM, Thursday 12-1PM room BE-353B, Wednesdays 4-5PM (BE354, George)

CANVAS COURSE WEBPAGE: Click HERE and follow the instrcutions

LECTURE NOTES: 

  • Numerical methods for ODEs (PDF)
  • Numerical methods for PDEs (PDF)

Grading Policy: 50% homework assignments, 50% final exam. 

Reference Books 

  • E. Hairer, S. P. Norsett and G. Wanner, ``Solving ordinary differential equations I: nonstiff problems'', Springer 2008 (book
  • Quarteroni, Salieri, Sacco ``Numerical mathematics'', Springer 2007 (book)
  • J. C. Strikwerda, ``Finite difference schemes and partial differential equations'', SIAM 2004 (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)
  • G. E. Karniadakis and S. Sherwin, ``Spectral-hp element methods for CFD'', Oxford 1999
  • J. D. Lambert, ``Numerical methods for ordinary differential equations: the initial value problem'', Wiley & Sons, 1991.