A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup

Rola Ali Ahmad, Toufic El Arwadi, Houssam Chrayteh and Jean-Marc Sac-Epée

Journal of Applied Mathematics, 2015, vol. 2015, 1-5

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 finite element scheme for the problem, and we illustrate this convergence by means of a FreeFem++ implementation.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:429641

DOI: 10.1155/2015/429641

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