Abstract
In this paper, we introduce a new implementation of the “parareal” time discretization aimed at solving unsteady nonlinear problems more efficiently, in particular those involving non-differentiable partial differential equations. As in the former implementation [3], the main goal of this scheme is to parallelize the time discretization to obtain an important speed up. As an application in financial mathematics, we consider the Black-Scholes equations for an American put. Numerical evidence of the important savings in computational time is also presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Chartier and B. Philippe (1993) A parallel shooting technique for solving dissipative ODE’s, Computing 51, pp 209–236.
J. Erhel J. and S; Rault S. (2000) Algorithme parallèle pour le calcul d’orbites, Techniques et Sciences informatiques, 19, pp 649–673.
J.-L. Lions, Y. Maday and G. Turinici (2001) Résolution d’EDP par un schéma en temps “pararéel”, C. R. Acad. Sci. Paris Sér. I Math. 332, no. 7, 661–668.
O. Pironneau, F. Hecht, D. Bernardi and K. Ohtsuka, FreeFem+, http://wwwrocq.inria.fr/Frederic.Hecht/FreeFemPlus.htm.
P. Wilmott, H. Howison and J. Dewynne (1998) Option Pricing. Mathematical models and computation, Oxford financial press, Oxford.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bal, G., Maday, Y. (2002). A “Parareal” Time Discretization for Non-Linear PDE’s with Application to the Pricing of an American Put. In: Pavarino, L.F., Toselli, A. (eds) Recent Developments in Domain Decomposition Methods. Lecture Notes in Computational Science and Engineering, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56118-4_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-56118-4_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43413-9
Online ISBN: 978-3-642-56118-4
eBook Packages: Springer Book Archive