SOLUTION TO ELLIPTIC-EQUATIONS USING THE SHIFT METHOD

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) (R(N)). Compared to the classic Monte carlo method the shift t urns out to be an efficient process in many aspects, especially when t aking account its implementation on computers. We recall that the rate of convergence of this method is given by theorems like the law of th e iterated logarithm and a central limit theorem. We try to apply this process to the numerical resolution of elliptiques equations. One goa l of this paper is to see, with ordinary example, how we can use the s hift in this case. Indeed, three techniques will be discussed and effi ciency will be tested by simulation, especially in comparison with the classic Monte Carlo method. Theoretical justifications will be shown.