Boletín SEMA, No 44 (2008)

Tamaño de la letra:  Pequeña  Mediana  Grande

THE NUMERICAL SOLUTION OF DISCONTINUOUS IVPS BY RUNGE–KUTTA CODES: A REVIEW

M. Calvo, J. I. Montijano, L. Rández

Resumen


In this paper several techniques for handling discontinuous IVPs when
they are solved by means of adaptive Runge–Kutta codes are examined.
The aim of the techniques is to provide, in an easy way, a tool to get
a precise location of the detected discontinuities and a crossing of them
retaining the accuracy of the numerical solution. Two remarkable features
of these techniques is that they do not require an a priori knowledge about
the location of the discontinuities and also that add a valuable capability
to the existing software with a small computational cost. Some numerical
experiments are presented to illustrate the reliability and efficiency of the
proposed algorithms.

Key words: Discontinuous Initial Value Problems, Adaptive Runge–Kutta
methods, Detection, location and crossing of discontinuities

AMS subject classifications: 65L06 65L05

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