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Foil 14 Estimate of Local Error in Euler's Method

From Parallel Programming for Particle Dynamics Extra Foils Computational Science CPS615 -- Spring 2000 Semester. by Geoffrey C. Fox
Let X(ti) be numerical solution and Y(ti) the exact solution. We have Taylor Expansion
And by assumption X(ti) = Y(ti) and in Euler's method we use exact derivative at ti. Thus And so X(ti+h) = Y(ti+h) + O(h2) and so local error is O(h2)
Accumulating this error over 1/h steps gives a global error of order h

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