For some methods, but not all, the degree of exactness is one less than the order of accuracy. Is that the case for the midpoint rul
For some methods, but not all, the degree of exactness is one less than the order of accuracy. Is that the case for the midpoint rul
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For some methods, but not all, the degree of exactness is one less than the order of accuracy. Is that the case for the midpoint rule?
Expert Solution
Step 1
Here, in the question, it is being conveyed that the degree of exactness is one less than the order of accuracy. The midpoint rule is a method for approximating integration that only considers the value of the function at its halfway. It is precise to second order. Use a single interval (i.e., ) and estimate the integrals of the test functions over to investigate the degree of precision of the midpoint technique. Each time, the exact answer is 1.
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