Theoretical Numerical Analysis: An Introduction to Advanced Techniques by Peter Linz

Author:Peter Linz
Language: eng
Format: epub
Publisher: Dover Publications, Inc.
Published: 2019-03-14T16:00:00+00:00

Applying rmn to the last equation, subtracting from (4.58) and using (4.57) we get

The left-hand side is the difference (in Xn) between the two computed solutions; the first term on the right-hand side is of the same order of magnitude as the dominant part of the error. This provides some justification for taking the difference between the two computed solutions as an approximation to the discretization error. We can do even better: multiply (4.59) by αp, apply rmn, and subtract from (4.58). Then

Thus the extrapolated solution

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