Highly stable parallel Volterra Runge-Kutta methods
A new family of parallel \(V\)-stable methods for second kind Volterra integral equations are investigated. In the author's previous works, the parallel iterated Volterra Runge-Kutta (PIVRK) method and the transformed Volterra Runge-Kutta method (TVRK) have been introduced [cf. \textit{E. Crisci}, \textit{E. Russo}, \textit{P. J. Van der Houwen} and \textit{A. Vecchio}, J. Comput. Appl. Math. 45, No. 1-2, 169-180 (1993; Zbl 0802.65133)]. In this paper a parallel method having better stability characteristics than the above-mentioned PIVRK and less cost than the TVRK methods is constructed. The new method, called PTVRK (parallel transformed Volterra Runge-Kutta) method is \(V\)-stable. Many particular methods of order \(p\) ranging from 2 to 8 are listed. In the end, numerical experiments are performed.
parallel iterated Volterra Runge-Kutta method
scientific article; zbMATH DE number 910313
scientific article