Overview
Longberg seasoning formula is also known as a semi-acceleration method. It is based on the relationship between trapezoidal formula, Simpson formula and Cooks formula, is constructed to accelerate the calculation integration. As an external estimate, it improves the accuracy of the error without increasing the amount of calculation.
In the case of equivalence base points, the calculation of the interstitial value is usually carried out by means of a method of dividing the interval. In this way, the previous segmentation of the function is still available after sexy and easy to program.
Detection Process
can be seen by , you can get one by and Approximate formulas than and as the approximate calculation method of , you can get < / p> Take the SIMPSON formula. The restriction of the SIMPSON formula is superior to the restriction trapezoidal formula.
Rehabilization Error Elements of the SIMPSON formula
if < / Section> When the change is not large, ie .
So get
and Linear combination can get an approximate formula that is better than and . Through the verification, the upper right end item is . That is,
Of course, the Cotes formula is superior to the resolution of the SIMPSON formula.
Similar to the previous derivation, the right end items of the above formula .
called is the Romberg value. It can be suspicious, and the Romberg value is better than cotes value . Therefore, the points will be calculated using the romberg value, which will have a faster convergence speed.
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