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Numerical Solution of ODE (NMNV539) — Practicals (Winter Semester 2024/2025)

This course will explore various numerical methods for the solution of ODEs. The practicals will apply these methods using MATLAB.

Lectures

Thursday 9:00 – 10:30, K4 Sokolovská 83 Karlín

Lecture notes (will be constantly updated during the course): lecture_notes.pdf

Brief revision/summary notes: revision.pdf

Practicals

Thursday 10:40 – 12:10, K4 Sokolovská 83 Karlín

• 03.10.2024:
  • Exercises
  • dirfield.m; logistic.m; oscillator.m; pendulum.m; (Zip Archive)
  • Solutions: Question 2; Question 3; Question 4; Question 5;
• 10.10.2024:
  • Exercises
  • blowupex.m; catmouse.m; catmouseevents.m; collapseex.m; dirfield.m; run_catmouse.m; run_catmouseevents.m; (Zip Archive)
  • Solutions: Question 1; Question 3; Question 4; Question 5;
• 17.10.2024:
  • Exercises
  • compare.m; compare_eul.m; eul.m; ieuler.m; ieuler_newton.m; linsystem.m; linsystem_newton.m; logistic.m; oscillator.m; pendulum.m; popgrowth.m; rk_classical.m; runge.m; (Zip Archive)
  • Solutions: Question 1(a); Question 1(b); Question 1(c); Question 2; Question 3; Question 4;
• 24.10.2024:
  • Exercises
  • compare_adaptive.m; crank_nicholson.m; eul.m; heun.m; ieuler.m; linsystem.m; logistic.m; ode12.m; ode12_1.m; ode12_2.m; one_step_order.m; oscillator.m; overheads.m; rk_classical.m; runge.m; (Zip Archive)
  • Solutions: Question 1; Question 2;
• 31.10.2024:
  • Exercises
  • conv_analysis.m; gauss2.m; lin1p.m; logistic.m; ode23_orig.m; rk_classical.m; run_gauss2.m; (Zip Archive)
  • Solutions: Question 1; Question 2; Question 3;
• 07.11.2024:
  • Exercises
  • ab2.m; ab3.m; am2.m; am2_mod.m; conv_analysis.m; eul.m; linsystem.m; logistic.m; oscillator.m; rk_classical.m; run_ab.m; (Zip Archive)
  • Solutions: Question 1; Question 2; Question 3;
• 14.11.2024:
  • Exercises
  • am2.m; bdf2.m; bdf3.m; conv_analysis.m; linsystem.m; logistic.m; ms2.m; ny2.m; ny3.m; oscillator.m; pred_corr.m; rk_classical.m; run_bdf.m; run_ny.m; run_pred_corr.m; sat_ode.m; (Zip Archive)
  • Solutions: Question 1; Question 2; Question 3;
• 21.11.2024:
  • Exercises
  • eul.m; ieuler.m; run_vdpol.m; run_vdpol_linear.m; vdpol.m; vdpol_limit.m; vdpol_linear.m; vdpol_steady.m; (Zip Archive)
  • Solutions: Question 1; Question 2;
• 28.11.2024:
  • Exercises
  • comp_pendfric_lin.m; eul.m; pendfric.m; pendfric_euler.m; pendfric_interactive.m; pendfric_lin.m; pendfric_stab.m; rk_classical.m; rk_stab.m; (Zip Archive)
  • Solutions: Question 1; Question 2;
• 12.12.2024:
  • Exercises
  • bruss.m; bruss_stiff_estimate.m; fdode.m; mstep_stab.m; plot_ab_stab.m; plot_am_stab.m; run_bruss.m; run_fdode.m; (Zip Archive)

MATLAB

The practical classes require the use of MATLAB. The following notes provide a brief introduction to MATLAB:

• Notes
• Slides

The practicals for this course take place in the K4 computer laboratory, which has access to MATLAB.

If you wish to access MATLAB from your own computer the university has a Total Academic Headcount MATLAB license, which allows you to install MATLAB locally on your machine. Alternatively, with this license you can use MATLAB Online, which allows you to access a (lightweight) instance of MATLAB directly in your web browser; this should be sufficient for this course.

In order to install MATLAB locally, or access MATLAB Online, you must register for a MathWorks account using an email address ending with cuni.cz. Detailed instructions are available at cuni.cz/UKEN-1270.html.

Homework

There will be two homeworks during the course of the year. Obtaining credit for the practical course will involve completion of these homeworks with at least 50%.

1. Implicit RK Methods (Support Files). Deadline: 23.11.2024
2. Predictor/Corrector (Support Files). Deadline: 12.12.2024

Exam

The exam will consist of two parts - a written and oral exam.

Course credit for the practicals must be obtained in order to enroll for the exam.

Two exam dates for the written exam are available to register via SIS:

• Tuesday January 14, 14:00-15:30, K7
• Monday January 27, 14:00-15:30, K7