Sunday, May 11, 2014

The Variable step Method of Fehlberg

In order to incorporate a variable step algorithm for the Fehlberg’s method, an equation for error estimation has to be included. The Butcher tableau (ref: Hairer, Nørsett & Wanner, Solving ODEs, Vol. 1, Non-stiff problems) with the ycap coefficients are:

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The generalized RK method can then be used with the Kaps-Rentrop algorithm for adaptive step size to solve ODEs.                                                                                                                       
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2 comments:

  1. Variable step Fehlberg’s Method –example | A Handful Of Numerical Integration TechniquesMay 14, 2014 at 8:20 PM

    […] Methods, ACM Trans. On Mathematical Software, Vol. 13, No. 1, 1987, pp 1-27) was solved using the Variable-Step Fehlberg’s method. The equations […]

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  2. Is the higher order Rosenbrock method worth the effort? | A Handful Of Numerical Integration TechniquesJuly 13, 2014 at 12:08 PM

    […] the solution is obtained from t= 0 to 500, with TOL = 1E-5 in about 715 steps. In contrast, the RK-Fehlberg algorithm takes over 12,400 steps to barely solve for the entire […]

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