The modified Simpson's rule for line integrals (Q2748173)
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scientific article; zbMATH DE number 1658946
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The modified Simpson's rule for line integrals |
scientific article; zbMATH DE number 1658946 |
Statements
19 August 2002
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continuation methods
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implicitly defined curve
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modified Simpson's rule
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global discretization error
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asymptotic error expansion
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modified Runge Kutta methods
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modified trapezoidal rule
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line integral
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numerical results
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0.93535805
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0.8804047
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0.85886866
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0.84949195
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0.8462093
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0.8433624
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0.8415501
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The modified Simpson's rule for line integrals (English)
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The modified trapezoidal rule for evaluating the line integral of a vector field over an implicitly defined curve is studied. This rule was given by \textit{H. I. Siyyam} and \textit{M. I. Syam} [J. Comput. Appl. Math. 84, No. 1, 1-14 (1997; Zbl 0885.65017)]; their results were satisfactory and not very accurate. A modified Simpson's rule for evaluating the line integral is developed in this paper. The global discretization error of this rule is \(O(h^4)\). An asymptotic error expansion of this rule is studied. Some numerical results are also given.
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