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By above discussion I try to clarify that local truncation error is a mean by which we can compare methods to find out what amount of error each method can produce, and hence local truncation error is very different from truncation error.
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Unlike truncation error which only indicates that error is due to taking small step sizes, local truncation error give us error in terms of complexity theory.
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I'm going to work on this article locally, where I'll introduce local and global truncation errors. I will also mention how they're linked (i.e. lipshitz).
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so local truncation error for Euler Method is O(h), for Heun's Method is O(h) and for Runge-Kutta Method is O(h).
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e.g. If Taylor method of order n is used to approximate a solution to y(t) = f(t, y(t)), a]t]b, y(a)=a
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When we have sin(x) = x + R(x), the remainder or chopped portion R(x) is known as truncation error.
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with step size h and if y Є C, then the local truncation error is O(h).
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Please read section 5.3 of reference book indicated in the article.
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