Numerical Methods for Partial Differential Equations

wisL602, Fall 2026

Lecturer: Dr. P.A. Zegeling, room 513, Math. Building (= HF-Building), Budapestlaan 6, Utrecht (030-2533720).

Venue: Universiteit Utrecht , Princetonplein 5, Utrecht Buys Ballotgebouw : room BBG005 (except in Week 41 ==> room DDW 1.16: David de Wiedgebouw)

Time:
14:00-15:45 theory/lectures
16:00-16:45 exercises/tutorial

Teaching assistant: Aurora
==> For questions about the weekly exercises you could also contact Aurora via: numpde2026ATgmail.com.

Literature: "LECTURE NOTES" and extra info (check the box "EXTRA MATERIAL"). The weekly schedule below will be updated weekly.

-- The book "Finite Difference Methods for Ordinary and Partial Differential Equations" by Randall J. LeVeque, 2007 could be very helpful. You can find the pdf file here.

Additional useful references/books that are closely related to the topics of the course are:
-- W. Hundsdorfer and J.G. Verwer (Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations; Springer 2003)
-- A. Tveito and R. Winther (Introduction to Partial Differential Equations, a Computational Approach; Springer 1998)
-- J.C. Strikwerda (Finite Difference Schemes and Partial Differential Equations; SIAM 2009)
-- J.W. Thomas (Numerical Partial Differential Equations, Finite Difference Methods; Springer 1998).


Grade: the final grade (FG) will be based on 15% assignment/computer exercise "C1", 15% computer exercise "C2" and 70% the final EXAM (tentamen) TT
===> FG = 0.05*C1A + 0.10*C1B + 0.15*C2 + 0.7*TT.


DATE LECTURES LECTURE NOTES EXERCISES EXTRA MATERIAL
Wednesday September 9 NO LECTURE TODAY due to the public transport strike! we start with Lecture 1 on Wednesday September 16, 14:00
Wednesday September 16 Lecture 1: intro PDEs (well-posedness, classification, Fourier method, method of characteristics) Lecture notes 1 Exercises 1 Extra file for Lecture 1
Wednesday September 23 Lecture 2: finite difference matrices Lecture notes 2 Exercises 2 Extra file 1 for Lecture 2
Extra file 2 for Lecture 2
Extra file 3 for Lecture 2 (cyclic shift matrices; periodic BCs)
Wednesday September 30 Lecture 3: time-integration and the method-of-lines Lecture notes 3 Exercises 3 Extra file 1 for Lecture 3
Extra file 2 for Lecture 3 (on LM-methods)
Extra file 3 for Lecture 3 (on RK-methods)
Wednesday October 7 Lecture 4: the heat equation Lecture notes 4 Exercises 4 Extra file for Lecture 4
Assignment C1A (5% of FG).
Wednesday October 14 Lecture 5: the advection equation Lecture notes 5 Exercises 5 Extra file 1 for Lecture 5
Extra file 2 for Lecture 5
Wednesday October 21 Lecture 6: the wave equation and nonlinear hyperbolic PDEs Lecture notes 6 Exercises 6 Extra file 1 for Lecture 6
Extra file 2 for Lecture 6 (on the wave equation)
Extra file 3 for Lecture 6 (on the MoCh for Burgers' equation)
Extra file 4 for Lecture 6 (on numerics for Burger's equation)
Wednesday October 28 ==> Tutorial on assignment C1A and exercises from Lectures 1-6!
Wednesday November 4 Lecture 7: exact and non-standard finite differences Lecture notes 7 (available: Wednesday Nov 4)
DEADLINE for C1A: Wednesday November 4 23:59 (via e-mail as ONE pdf file to: numpde2026ATgmail.com).
Exercises 7 Extra file 1 for Lecture 7
Extra file 2 for Lecture 7
Assignment C1B (10% of FG).
Wednesday November 11 Lecture 8: Hamiltonian ODEs and PDEs Lecture notes 8 (available: Wednesday Nov 11) Exercises 8 Extra file 1 for Lecture 8
Extra file 2 for Lecture 8
Wednesday November 18 ==> Tutorial on assignment C1B and exercises from Lectures 7-8
Wednesday November 25 Lecture 9: Strang splitting and the Ginzburg-Landau PDE model; guest lecture 1 by Erwin Luesink DEADLINE for C1B: Wednesday November 25 23:59 (via e-mail as ONE pdf file to: numpde2026ATgmail.com; matlab/python codes in separate files in the same e-mail message).
Assignment C2 (15% of FG) ==> related to guest lectures 9 and 11(!) (available: Thursday November 26)
Wednesday December 2 Lecture 10: travelling waves and adaptive methods
Wednesday December 9 Lecture 11: Numerical solution of stochastic differential equations; guest lecture 2 by Chiheb Ben Hammouda
Wednesday December 16 Lecture 12: fractional order PDEs and boundary-value methods and exercises from Lectures 10 and 12 DEADLINE for C2: Wednesday December 16 23:59 (via e-mail as ONE pdf file to: numpde2026ATgmail.com; matlab/python codes in separate files in the same e-mail message).
Wednesday January 20, 2027 EXAM (on Lectures 1-8, 10, 12)
Wednesday February 17 2027 RETAKE (on Lectures 1-8, 10, 12)