Assume that S ( h ) is equivalent to the (composite) Simpson's rule where h is the size of the step. Correct use of Richardson's extrapolation gives the formula: R ( h ) = 16 S ( h ) − S ( a ) b . What's a and b?

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Assume that   S  (  h  ) is equivalent to the (composite) Simpson&#039;s rule where h is the size of the step. Correct use of Richardson&#039;s extrapolation gives the formula:   R  (  h  )  =            16      S      (      h      )      −      S      (      a      )        b  . What&#039;s a and b?

cegielnikmzjkf · Accepted Answer

Given a method   A  (  h  )  =      α    0    +      α    1        h    k    +      O    (      h          k      +      1        ) that approximates       α    0  , the idea is to combine   A at varying step sizes to eliminate the lowest power of   h, say       h    k  .Since the error of Simpson&#039;s rule is       O    (      h    4    ), we have   S  (  h  )  =      α    0    +      α    1        h    4    +      O    (      h    5    ) and                    16        S        (        h        )                            =        16                  α          0                +        16                  α          1                          h          4                +                  O                (                  h          5                )                            S        (        2        h        )                            =                  α          0                +        16                  α          1                          h          4                +                  O                (                  h          5                )            which implies  16  S  (  h  )  −  S  (  2  h  )  =  15      α    0    +      O    (      h    5    )  .

Assume that S ( h ) is equivalent to the (composite) Simpson's rule where h is the si

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