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2015 A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup
Rola Ali Ahmad, Toufic El Arwadi, Houssam Chrayteh, Jean-Marc Sac-Epée
J. Appl. Math. 2015: 1-5 (2015). DOI: 10.1155/2015/429641

Abstract

The aim of this work is to study a semidiscrete Crank-Nicolson type scheme in order to approximate numerically the Dirichlet-to-Neumann semigroup. We construct an approximating family of operators for the Dirichlet-to-Neumann semigroup, which satisfies the assumptions of Chernoff’s product formula, and consequently the Crank-Nicolson scheme converges to the exact solution. Finally, we write a P 1 finite element scheme for the problem, and we illustrate this convergence by means of a FreeFem++ implementation.

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Rola Ali Ahmad. Toufic El Arwadi. Houssam Chrayteh. Jean-Marc Sac-Epée. "A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup." J. Appl. Math. 2015 1 - 5, 2015. https://doi.org/10.1155/2015/429641

Information

Published: 2015
First available in Project Euclid: 17 August 2015

zbMATH: 07132065
MathSciNet: MR3370964
Digital Object Identifier: 10.1155/2015/429641

Rights: Copyright © 2015 Hindawi

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