On the solution of discontinuous IVPs by adaptive Runge-Kutta codes
Calvo, M. (email@example.com) ; Montijano, Juan I. (firstname.lastname@example.org) ; Rández, Luis (email@example.com)
Published in: Numerical Algorithms
Numer. Algorithms Vol. 33, Num. 1-4 (agosto de 2003), pp. 163-182
Abstract: In this paper an automatic technique for handling discontinuous IVPs when they are solved by means of adaptive Runge–Kutta codes is proposed. This technique detects, accurately locates and passes the discontinuities in the solution of IVPs by using the information generated by the code along the numerical integration together with a continuous interpolant of the discrete solution. A remarkable feature is that it does not require additional information on the location of the discontinuities. Some numerical experiments are presented to illustrate the reliability and efficiency of the proposed algorithms.
Department: Matemática Aplicada
Keyword(s): discontinuous initial value problems ; adaptive Runge–Kutta methods ; detection of discontinuities
Record created 2009-05-07, last modified 2011-08-09