Résolution des équations elliptiques par la méthode du shift

✍ Scribed by Mohamed Ben Alaya

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 478 KB
• Volume: 38
• Category: Article
• ISSN: 0378-4754
• DOI: 10.1016/0378-4754(93)e0070-l

✦ Synopsis

The pointwise Birkhoff theorem applied with the shift operateur on ]R N yields a new practical method to compute expectation of functionals in L 1 (RN). Compared to the classic Monte carlo method the shift turns out to be an efficient process in many aspects, especially when taking account its implementation on computers. We recall that the rate of convergence of this method is given by theorems like the law of the iterated logarithm and a central limit theorem.

We try to apply this process to the numerical resolution of elliptiques equations. One goal of this paper is to see, with ordinary example, how we can use the shift in this case. Indeed, three techniques will be discussed and efficiency will be tested by simulation, especially in comparison with the classic Monte Carlo method. Theoretical justifications will be shown.

Dans la suite on notera par IR ~r~ l'espace produit de IR, ~ =/z ®N la mesure produit d6finie sur ~®r~ 06 Iz est une probabilit6 sur ~, et 0 la fonction de d6calage, appel6e aussi op6rateur de shift, d6finie sur IR ®r~ par o(Y~, Y2 ..... Yk ....