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Saturday, November 21, 2015

Scientific Computing - Quiz 1 - Question 5

Problem:

Using Eqs.~(1.1.10)-(1.1.12) found in the lecture notes found under the course resource link, derive the three important schemes: Heun's method (A = 1/2), modified Euler-Cauchy (A = 0) and Euler (A = 1).

Solution:

Here is the link to the full lecture notes:

The derivation based on 1.1.12 is pretty easy, for Heun's method:

A+B=1B=12.
PB=12P=1.
BQ=12Q=1.

For Euler-Cauchy method:

A+B=1B=1.
PB=12P=12.
BQ=12Q=12.

For Euler method:

A+B=1B=0.
P and Q are meaningless in the context of the iteration, we do not want any correction at all in this case.

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