Risorsa Analitica di Seriale

The present paper is the continuation of a previous one [I], in which two problems are discussed. In the first problem, approximate values of a function u = ui», y) and of its tangential and normal derivatives are supposed to be known on the boundary C of a star–shaped region G. The function u is supposed to be biharmonic in G, and an approximation of u in G is sought. In the second problem, the same data as above are supposed to be known at the boundary of a region GI' contained in G, and an approximation to the biharmonic function u in G is again sought. In this paper some examples of numerical solution of the two problems are given in the case that GI' ancl Gare ellipses. The solution processes described in the following pages make use of "linear programming" and "least squares" techniques. Results are discussed and the efficiency of the methods is compared.