Title: Parallel solution of the discretised and linearised G-heat equation

Authors: Pierre Spiteri; Amar Ouaoua; Ming Chau; Hacène Boutabia

Addresses: ENSEEIHT-IRIT, 2 rue Charles Camichel, 31071 Toulouse CEDEX, France ' Laboratoire LaPS, Badji Mokhtar University, P.O. Box 12, 23 000 Annaba, Algeria ' Advanced Solutions Accelerator, 199 rue de l'Oppidum, 34170 Castelnau le Lez, France ' Laboratoire LaPS, Badji Mokhtar University, P.O. Box 12, 23 000 Annaba, Algeria

Abstract: The present study deals with the numerical solution of the G-heat equation. Since the G-heat equation is defined in an unbounded domain, we firstly state that the solution of the G-heat equation defined in a bounded domain converges to the solution of the G-heat equation when the measure of the domain tends to infinity. Moreover, after time discretisation by an implicit time marching scheme, we define a method of linearisation of each stationary problem, which leads to the solution of a large scale algebraic system. A unified approach analysis of the convergence of the sequential and parallel relaxation methods is given. Finally, we present the results of numerical experiments.

Keywords: G-heat equation; relaxation methods; parallel computing; asynchronous iteration; financial application.

DOI: 10.1504/IJHPCN.2018.088880

International Journal of High Performance Computing and Networking, 2018 Vol.11 No.1, pp.66 - 82

Received: 02 Nov 2015
Accepted: 20 Feb 2016
Published online: 22 Dec 2017 *

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