Numerical Methods for Partial Differential Equations

wisL602, Spring 2025

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

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

Teaching assistant: Jelle van der Voort
==> For questions about the weekly exercises you could also contact Jelle via: numpde2025ATgmail.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" (5% "C1A", 10% "C1B"), 15% computer exercise "C2" (10% "C2A", 5% "C2B") and 70% the final EXAM (tentamen) TT, i.e. FG = [0.05*C1A+0.10*C1B] + [0.10*C2A+ 0.05*C2B] + 0.7*TT.


DATE LECTURES LECTURE NOTES EXERCISES EXTRA MATERIAL
Tuesday February 4 Lecture 1: intro PDEs (well-posedness, classification, Fourier method, method of characteristics, applications) Lecture notes 1 Exercises 1 Extra file for Lecture 1
Tuesday February 11 Lecture 2: finite difference matrices Lecture notes 2 Exercises 2 Extra file for Lecture 2
Tuesday February 18 Lecture 3: time-integration and the method-of-lines Lecture notes 3 Exercises 3 Extra file for Lecture 3
Tuesday February 25 ==> Tutorial on assignment C1A Assignment C1A (5% of FG). Please check some minor changes and extra hints in the updated file on Friday 28-2-2025.
Tuesday March 4 Lecture 4: the heat equation Lecture notes 4 Exercises 4 Extra file for Lecture 4
Tuesday March 11 Lecture 5: the advection equation Lecture notes 5 Exercises 5
DEADLINE for C1A: Tuesday March 11 23:59 (via e-mail as ONE pdf file to: numpde2025ATgmail.com).
Extra file for Lecture 5
Tuesday March 18 ==> Tutorial on computer exercise C1B Computer exercise C1B (10% of FG)
Tuesday March 25 Lecture 6: the wave equation and nonlinear hyperbolic PDEs Lecture notes 6 Exercises 6 Extra file for Lecture 6
Tuesday April 1 Lecture 7: exact and non-standard finite-differences Lecture notes 7 Exercises 7 Extra file for Lecture 7
Tuesday April 8 Lecture 8: fractional order PDEs and boundary-value methods Lecture notes 8 Exercises 8
DEADLINE for C1B: Tuesday April 8 23:59 (via e-mail as ONE pdf file + codes in a separate file to: numpde2025ATgmail.com).
Fractional DEs:
Extra file 1 for Lecture 8
Extra file 2 for Lecture 8
Extra file 3 for Lecture 8
Extra file 4 for Lecture 8
Boundary-value methods:
Extra file 5 for Lecture 8
Extra file 6 for Lecture 8
Extra file 7 for Lecture 8
Tuesday April 15 ==> Tutorial on computer exercise C2A Computer exercise C2A (10% of FG)
Tuesday April 22 Lecture 9: Hamiltonian ODEs and PDEs Lecture notes 9 Exercises 9 Extra file 1 for Lecture 9
Extra file 2 for Lecture 9
Tuesday April 29 Lecture 10: the inverse heat (and inverse wave) equation (guest lecturer: Tristan van Leeuwen) Lecture notes 10 (available April 29) Computer exercise C2B on Lecture 10 (5% of FG).
Tuesday May 6 Lecture 11: finite elements: stationary and time-dependent Lecture notes 11 (available May 6) Exercises 11 (available May 6)
DEADLINE for C2A: Tuesday May 6 23:59 (via e-mail as ONE pdf file + codes in a separate file to: numpde2025ATgmail.com).
Extra file for Lecture 11 (available May 6)
Tuesday May 13 Tutorial on a selected set of exercises from lectures 1-11, except lecture 10: exercises..., ..., ...(TBD)
Tuesday May 20 Lecture 12: travelling waves and adaptive methods Lecture notes 12 (part 1)
Lecture notes 12 (part 2)
Lecture notes 12 (part 3) (available May 20)
Exercises 12 (available May 20)
DEADLINE for C2B: Tuesday May 20 23:59 (via e-mail as ONE pdf file + codes in a separate file to: numpde2025ATgmail.com).
Extra file 1 for Lecture 12
Extra file 2 for Lecture 12 (available May 20)
Tuesday May 27 TBD
Tuesday June 3 EXAM ("TENTAMEN") (this is a closed book exam!): based on all lectures
and exercises, except lecture 10 and except the optional parts
(marked by "*"-s in the exercises sheets and lecture notes).
LOCATION: DALTON 500 - 1.27 (Daltonlaan 500, 3584 BK Utrecht)
Tuesday June 24 RETAKE ("HERTENTAMEN") (this is a closed book exam!): based on all lectures
and exercises, except lecture 10 and except the optional parts
(marked by "*"-s in the exercises sheets and lecture notes).
LOCATION: RUPPERT - 031 (Leuvenlaan 21, 3584 CE Utrecht)