A fourth order extrapolation for the trapezoidal rule (Q1282127)
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scientific article; zbMATH DE number 1269902
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A fourth order extrapolation for the trapezoidal rule |
scientific article; zbMATH DE number 1269902 |
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A fourth order extrapolation for the trapezoidal rule (English)
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1 August 1999
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Denote by \(\{ y_n \}\) the numerical solution of a stiff differential equation obtained by the trapezoidal rule. In order to improve the accuracy of this approximation, the authors propose to add a correction term which can be computed by a linear recurrence relation that depends on \(\{ y_n \}\) and on the Jacobian of the problem. A linear stability analysis shows that the new approximation retains the A-stability. Numerical experiments are included which confirm the stability and the higher order of the new algorithm.
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stiff differential equations
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A-stability
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trapezoidal rule
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fourth-order extrapolation
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numerical experiments
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algorithm
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