Numerical Methods for Time-Dependent Partial Differential Equations

wisL602, Spring 2024

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

Venue: Universiteit Utrecht , Budapestlaan 6, Utrecht, HF-Building : room 611AB

Time:
10:00-11:45 theory/lectures
12:00-12:45 exercises/tutorial

Teaching assistant: Quirijn Kokkeler

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

-- 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% computer exercise "C1", 15% hand-in exercise "C2" and 70% the final EXAM (tentamen) TT, i.e. FG = 0.15*C1+0.1*C2A+0.05*C2B+0.7*TT.



DATE LECTURES LECTURE NOTES EXERCISES EXTRA MATERIAL
February 7 Lecture 1: intro PDEs + basic tools Lecture notes 1 Exercises 1
Solutions 1
Extra file for Lecture 1
February 14 Lecture 2: finite difference approximations Lecture notes 2 Exercises 2
Solutions 2
Extra file for Lecture 2
February 21 Lecture 3: time-integration methods and the method-of-lines Lecture notes 3 Exercises 3
Solutions 3
Extra file for Lecture 3
February 28 Lecture 4: the heat equation Lecture notes 4 Exercises 4
Solutions 4
Extra file for Lecture 4
March 6 Lecture 5: the advection equation Lecture notes 5 Exercises 5
Solutions 5
Extra file for Lecture 5
March 13 Lecture 6: the wave equation and nonlinear hyperbolic PDEs Lecture notes 6 Computer exercise C1 (15% of FG)
Exercises 6
Solutions 6
Extra file for Lecture 6
March 20 ==> From 11:00-12:45: questions can be asked about C1 in room 611AB
March 27 Lecture 7: Non-standard finite-differences, splitting and (*)exponential methods Lecture notes 7 Exercises 7
Solutions 7
Extra file 1 for Lecture 7
Extra file 2 for Lecture 7
Extra file 3 for Lecture 7
April 3 Lecture 8: Hamiltonian ODEs and PDEs Lecture notes 8 DEADLINE for Computer exercise C1 (a printed version in room 611AB or via e-mail as ONE pdf file + codes in a separate file)
Exercises 8
Solutions 8
Extra file 1 for Lecture 8
Extra file 2 for Lecture 8
April 10 Lecture 9: Fractional order PDEs and boundary-value methods Lecture notes 9 Computer exercise C2A (10% of FG)
Exercises 9
Solutions 9
Matlab file for Exercise 9.3(b)
Extra file 1 for Lecture 9
Extra file 2 for Lecture 9
Extra file 3 for Lecture 9
Extra file 4 for Lecture 9
Extra file 5 for Lecture 9
Extra file 6 for Lecture 9
April 17 Lecture 10: Finite element methods for PDEs Lecture notes 10 Exercises 10
Solutions 10
Extra file for Lecture 10
April 24 Lecture 11: Travelling waves and higher-order PDEs Lecture notes 11 Exercises 11
Solutions 11
Extra file 1 for Lecture 11
Extra file 1 for Lecture 11
May 1 Lecture 12: Non-uniform and adaptive methods Lecture notes 12 Part I
*Lecture notes 12 Part II
*Lecture notes 12 Part III
*Lecture notes 12 Part IV
Exercises 12
Solutions 12
Extra file 1 for Lecture 12
Extra file 1 for Lecture 12
Extra file 3 for Lecture 12
May 8 Lecture 13: (*)Inverse PDE problems => C2B!
(guest lecturer: Dr. Felix Lucka, CWI)
*Lecture notes 13 Computer exercise C2B (5% of FG)
The Matlab files can be found in the pdf file of the exercise; Python files for Part B: see below!
DEADLINE for Computer exercise C2A (a printed version in room 611AB or via e-mail as ONE pdf file + codes in a separate file)
May 15 Lecture 14: (*)Stochastic differential equations => C2B!
(guest lecturer: Dr. Chiheb Ben Hammouda, UU).
*Lecture notes 14 Additional files (Python) for computer exercise C2B Part B can be found here.
May 22 NO MEETING TODAY! DEADLINE for Exercise C2B PART A (via e-mail as ONE pdf file + codes in a separate file)
May 29: 10:00-11:45 Exercises from lectures 1-12 AND questions from the Mock Exam will be discussed.
(solutions can be found here; available: May 30)
LOCATION: room 611AB!!! DEADLINE for Exercise C2B PART B (via e-mail as ONE pdf file + codes in a separate file)
June 5 EXAM ("TENTAMEN") (this is a closed book exam!): based on all lectures
and exercises, except lectures 13 and 14 and except the optional parts
(marked by "*"-s in the exercises sheets and lecture notes).
LOCATION: EDUC - ALFA TIME: 10:00-13:00
extra time students at another location!
June 26 RETAKE ("HERTENTAMEN") (this is a closed book exam!): based on all lectures
and exercises, except lectures 13 and 14 and except the optional parts
(marked by "*"-s in the exercises sheets and lecture notes).
LOCATION: BBG - 017 TIME: 10:00-13:00