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=1⟹B=12.
PB=12⟹P=1.
BQ=12⟹Q=1.
For Euler-Cauchy method:
A+B=1⟹B=1.
PB=12⟹P=12.
BQ=12⟹Q=12.
For Euler method:
A+B=1⟹B=0.
P and Q are meaningless in the context of the iteration, we do not want any correction at all in this case.
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=1⟹B=12.
PB=12⟹P=1.
BQ=12⟹Q=1.
For Euler-Cauchy method:
A+B=1⟹B=1.
PB=12⟹P=12.
BQ=12⟹Q=12.
For Euler method:
A+B=1⟹B=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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