Understand Truncation Order 2: Conditions & Examples

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SUMMARY

The discussion centers on understanding truncation order, specifically order 2, in the context of numerical methods. Dan initially sought clarification on whether demonstrating that a function is twice differentiable is sufficient to establish a truncation order of 2 for the prediction-correction method. He later concluded that two specific conditions must be satisfied to confirm this truncation order. Additionally, Dan expressed confusion regarding the concept of truncation, linking it to the accuracy of area calculations.

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  • Understanding of numerical methods, particularly prediction-correction methods.
  • Knowledge of differentiability and its implications in calculus.
  • Familiarity with truncation error concepts in numerical analysis.
  • Basic grasp of accuracy in numerical integration techniques.
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  • Research the conditions for establishing truncation order in numerical methods.
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Students and professionals in mathematics, engineering, and computer science who are involved in numerical analysis and seek to deepen their understanding of truncation orders and their implications in numerical methods.

nacho-man
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I do not understand how to do the question in part b.

Suppose I show that the function is twice differentiable (how do i do so), is that sufficient to show that the 'method' (does this refer to the prediction-correction method) has a truncation order of 2?

What is truncation?

Please see attached image.
I have the solutions for this question, however I do not understand them one bit. If anyone would like me to post them, I'd be more then happy too.

thanks
EDIT: I've solved this.

In order to show for a truncation of order 2, there are two conditions which must be satisfied. That is all the question is asking.

Thanks anyway.
 

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So what is meant by "truncation?" My journey into the depths of Google didn't really get me anywhere. I know it has to do with the accuracy of the area calculation, but couldn't get further than that.

-Dan
 

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