Keyword | CPC | PCC | Volume | Score | Length of keyword |
---|---|---|---|---|---|

richardson extrapolation trapezoidal rule | 0.74 | 0.6 | 5223 | 35 | 41 |

richardson | 0.32 | 0.4 | 915 | 45 | 10 |

extrapolation | 1.04 | 0.1 | 9740 | 97 | 13 |

trapezoidal | 1.69 | 0.6 | 1613 | 67 | 11 |

rule | 0.87 | 0.8 | 1591 | 54 | 4 |

Richardson’s Extrapolation Formula for Trapezoidal Rule The true error in a multiple segment Trapezoidal Rule with n segments for an integral (1) is given by (2) where for each i, is a point somewhere in the domain , and the term can be viewed as an approximate average value of in . This leads us to say that the true error, Et in Equation (2) (3)

Practical applications of Richardson extrapolation include Romberg integration, which applies Richardson extrapolation to the trapezoid rule, and the Bulirsch–Stoer algorithm for solving ordinary differential equations. A ( h ) = A ∗ + C h n + O ( h n + 1 ) . {\displaystyle A (h)=A^ {\ast }+Ch^ {n}+O (h^ {n+1}).}

This pseudocode assumes that a function called Trapezoidal (f, tStart, tEnd, h, y0) exists which attempts to compute y (tEnd) by performing the trapezoidal method on the function f, with starting point y0 and tStart and step size h . Note that starting with too small an initial step size can potentially introduce error into the final solution.