Understand Truncation Order 2: Conditions & Examples

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In summary, The conversation discusses the concept of truncation order and how to show that a function is twice differentiable, which would prove the method has a truncation order of 2. The speaker also mentions they have solutions for the question but do not understand them and offers to share them. They ultimately solve the question and clarify what is meant by "truncation."
  • #1
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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  • #2
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
 

Related to Understand Truncation Order 2: Conditions & Examples

1. What is truncation order 2?

Truncation order 2 is a mathematical concept used to approximate a function or equation with a polynomial of degree 2 or less. It involves replacing higher order terms with lower order terms, which allows for simpler calculations and easier analysis.

2. What are the conditions for using truncation order 2?

The main condition for using truncation order 2 is that the function or equation being approximated must be smooth and continuous. This means that it must have a defined value at every point and have no abrupt changes or breaks. Additionally, the interval of approximation should be small enough to ensure accurate results.

3. How is truncation order 2 different from other approximation methods?

Truncation order 2 differs from other approximation methods, such as Taylor series and interpolation, in that it only uses terms up to degree 2. This makes it a simpler and more efficient method for approximating functions, especially when higher order terms have little impact on the overall result.

4. Can you provide an example of truncation order 2?

Let's say we want to approximate the function f(x) = cos(x) using truncation order 2 at x = 0. Using the first two terms of the Taylor series, we get f(x) = 1 - x^2/2. This is our polynomial of degree 2, which is a good approximation of cos(x) near x = 0.

5. What are the benefits of using truncation order 2?

Using truncation order 2 allows for simpler calculations and can provide a good approximation of a function or equation in a specific interval. It also helps in simplifying complex mathematical concepts and making them easier to understand and analyze. Additionally, truncation order 2 is a commonly used method in various fields such as physics and engineering.

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