## DME2C Lab 5: Runge-Kutta

DME2C are invited to do Lab 5: Runge-Kutta remotely.

I have set up an (ungraded) assignment on Canvas that you (DME2C student) can submit your Lab 5 work. After Tuesday 09:00 I will download all the submissions and give feedback on each.

Recall our overall framework for our programmes in MATH7016:

• Define variables
• Give initial values
• Loop that
• Prints current variables (of interest)
• Calculates next variables

For Runge-Kutta, as usual there will be an x and y variables, but also a number of $k_i$ variables which represent (estimates of) the slope at various points between the current and next value.

The loop must calculate the various $k_i$ BEFORE calculating the next and values. The next value is given as:

$y_{i+1}=y_i+h\cdot \phi(k_1,\dots,k_n)$,

where $\phi(k_1,\dots,k_n)$ is a weighted average of the slopes $k_i$. There is one for Euler’s Method (slope at previous), two for Heun’s (slope at previous and slope at predicted next), and we also look at ‘Common’ RK3 which uses three k variables, $k_1,\,k_2,\,k_3$, and ‘Classical’ (state-of-the-art) RK4 which uses four.

All of Lab 5 is to be done in VBA. Problem 4 is missing the formula:

$y_{i+1}=y_i+h\cdot \phi(k_1,\dots,k_4)$,

the relevant formula is on p. 74. Also the sign of the derivative is wrong (and I have the rocket fuel being ejected too quickly… use

$\displaystyle\frac{dv}{dm}=-\frac{5}{m}$.

## DME2C: Concept MCQ 5

I want to keep the (ungraded) MCQ league going — I have pledged €35 of my own cash for first (€20), second (€10), and third (€5), and it would be great to keep it going until the ‘end of the season’. The same three names have been leading the league for a few weeks so maybe they might falter now.

Well anyway, DME2C can enter MCQ5 by emailing me their selection (ABCDDB or whatever) before Tuesday 09:00.

## Week 8

Luckily enough from my point of view, because of St Patrick’s Day, I have already recorded lectures for next week.

First watch Goal Seek for Boundary Value Problems (less than 20 minutes).

Then you will be in a position to do Lab 6: Boundary Value Problems.

Between Tuesday 17 March and Monday 23 March, you will be able to submit your work to Canvas, from which I will give you individual feedback.

After this watch the rest of the first playlist, watch Intro to PDEs (less than 20 minutes), and then watch the Derivation of the Laplace Equation (40 minutes).

I will also send on an MCQ6 to keep the league going.

## Week 7

In the Tuesday 09:00 class we had Written Assessment 1.

The lab was based on Runge Kutta methods.

In the 12:00 lecture we did a (written) Shooting Method example.

In VBA we will also have MCQ V.

## MCQ League

Unless you are excelling, you are identified by the last five digits of your student number.

Please ask questions in the lab about questions you have gotten wrong. Students in red appear to not have a good handle on the material and should consider putting in extra time outside class in doing exercises (in the manuals).

DME2C have not yet had a chance to do MCQ V so this is the same table as last time out.

## Written Assessment 1

Results have been sent to you.

## Assessment

The following was a proposed assessment schedule.

Obviously I cannot provide certainty about assessment at this time.

1. Week 11, 20% Second VBA Assessment, Based (roughly) on Weeks 6-9
2. Week 12, 40% Written Assessment(s), Based on Weeks 1-11. Melbourn Hall, Tuesday 28 April, 15:00-17:00

## Study

Study should consist of

• doing exercises from the notes
• completing VBA exercises