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Volume 6, Issue 5, Article 141 |
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Integral Inequalities and Computer Algebra Systems
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Authors: |
John Roumeliotis, |
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Keywords:
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Symbolic computation, Numerical integration, Simpson's rule, Trapezoidal rule, Integral inequalities. |
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Date Received:
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27/05/05 |
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Date Accepted:
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01/12/05 |
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Subject Codes: |
Prim: 68W30, 65D30; Sec: 26D10, 26D15.
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Editors: |
Iosif Pinelis, |
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Abstract: |
Theoretical results involving approximation of integrals are often
established from the construction and resultant manipulation of an
appropriate kernel. The systematic use of these kernels has
produced an abundance of new approximations and error estimates in
terms of norms of the integrand. Notwithstanding the great success
of this approach, many approximations and error results have yet
to be discovered due to the algebraic complexities involved;
especially those that involve product integrands.
We outline a method that uses the computer algebra system Maple
that is able to recapture the well known Ostrowksi, trapezoidal
and Simpson's inequalities. Moreover, the technique, which
involves manipulation of the Peano kernel, can be adapted to
develop new rules.
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