Local Error: Euler/Modified Euler - moved

ChrisHuey

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Mar 17, 2018
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Hi All,

I know that it I substitute theta = 0, I get Euler method. If I substitute theta = 1/2, I get Crank-Nicholson. I know this means that Crank-Nicholson is more accurate, but I am unsure how to answer the part of the question concerning the attached ODE.

Is anyone able to help with this?

Thanks.
 

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1) Are you SURE you cannot find circumstances where each is the more accurate?

2) What's stopping you from calculating the specified partial derivatives?
 
1) Are you SURE you cannot find circumstances where each is the more accurate?

You probably can. But from the notes I do have that touches on this topic, I know the person will be wanting me to reduce it to the Euler and Crank-Nicholson method using those states theta values, and thus show Crank-Nicholson is more accurate.

Question is written in such a way that they are wanting me to show that one is more accurate than the other as well, so I am fine that this is what they are wanting.

2) What's stopping you from calculating the specified partial derivatives?

I don't know what I am being asked. What is Xn and Xn+1 in this particular case? I wouldn't know where to start on this bit as it is.
 
1) Are you SURE you cannot find circumstances where each is the more accurate?

2) What's stopping you from calculating the specified partial derivatives?

1) They are leading me to choose a more accurate method, and the only notes I have on this fill not even one page and simply state that the substituted theta values yield the Euler and Crank-Nicholson method. So I know they're expecting me to use that to show it's more accurate.

2) I honestly have no idea about this, which is what I am wanting help with. Not sure even how to start, such as what Xn or Xn+1 are. Otherwise I would have at least tried to differentiate and offer something.
 
1) Are you SURE you cannot find circumstances where each is the more accurate?

2) What's stopping you from calculating the specified partial derivatives?

Is the attached the first term of the LE using the given ODE? How to get the second term of LE?
 

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Local Error: Euler/Crank-Nicholson

Hi,

Is that the first term of the LE using the given ODE? If so, how to calculate the second term of the LE expression (i.e. third-order partial derivatives)?
 

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  • ODE.PNG
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  • ssss.jpg
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