Talk:Truncation error

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Please read section 5.3 of reference book indicated in the article.

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.

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)=a₀ with step size h and if y Є Cⁿ⁺¹[a,b], then the local truncation error is O(hⁿ).

so local truncation error for Euler Method is O(h), for Heun's Method is O(h²) and for Runge-Kutta Method is O(h⁴).

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.