Practicum Numerical Methods

# Practicum Numerical Methods

### Evaluation

• 50% Final theory exam
• 50% Permanent evaluation on exercises
• 10% Sent in solutions
• 10% Extra exercise
• 30% Small questions about exercises (oral)

When we stop working on a worksheet during the contact hours, I will mention when to hand in all your solutions. You will get time to finish unfinished exercises at home. Only one (unspecified) question will be checked for errors. The week after, we ask every student individually a few small questions about the made exercises. It should not be necessary to study for this, as long as you were able to solve the exercises yourselves.

### How to hand in your solutions

Please, send in your solutions in such a way that I can easily check the correctness of the solutions. E.g. if you write a function fun.m, also write an executable script to test the function. We suggest that you write for every exercise a separate executable script as shown below:

fact.m
``````function y=fact(x)
if x>1
y=fact(x-1)*x;
else
y=1;
end
end
``````
exercise1.m
``````%Exercise 1

% This gives indeed 120
``````
exercise2.m
``````%Exercise 2

``````
or you can put the results of all exercises in a single script file with multiple sections

fact.m
``````function y=fact(x)
if x>1
y=fact(x-1)*x;
else
y=1;
end
end``````
practicum1.m
``````%Practicum 1

%% Exercise 1
% This gives indeed 120

%% Exercise 2
``````

Zip or tar all function files and executable scripts and send it:

• misa.andelkovic@uantwerpen.be
with subject Practicum 1, 2...

Please, let us know if you use Octave or another clone of Matlab instead of Matlab.

### Worksheets

Practical 1: Finding solutions of non-linear equations October 1 October 2
Practical 2: Systems of linear equations
Practical 3: Interpolation and splines
Practical 4: Curve fitting
Practical 5: Numerical differentiation and integration
Practical 6: Ordinary differential equations with BC
Practical 7: Partial differential equations I
Practical 8: Partial differential equations II
Practical 9: Partial differential equations III
Practical 10: Partial differential equations IV
Practical 11: Time independent Schrödinger equation

### Extra exercise

There will be no questions on practical 10 and 11. Instead, I will ask you to solve the time-(in)dependent Schrödinger for a 'self-invented' problem. The extent of the problem should be similar to the extent of the problems seen in practical 10 and 11. Be creative and try to come up with something unique! Below is a list to sparkle your imagination.

• Time-dependent
• Interference of two particles (without interaction)
• Particle traveling on a potential hill
• Particle going back and forth in a parabolic potential or potential well
• Study of tunneling using a periodic varying Dirichlet boundary condition
• Modify the Schro.m script to solve the 2D time-dependent Schrödinger equation
• ...
• Time-independent
• Eigenstates of a potential well with a small barrier in the middle
• Eigenstates of a 2D or 3D potential well (see extra exercise on worksheet 11)
• Eigenstates of a 2D harmonic potential (see extra exercise on worksheet 11)
• Eigenstates of a Mexican hat
• Using a different basis than the one used in practical 11 (ask for information)
• Kronig-Penney model (difficult but very interesting)
• ...