489 research outputs found
On optimal quadrature formulae
No full text A procedure to construct quadrature formulae which are exact for solutions of linear differential equations and are optimal in the sense of Sard is discussed. We give necessary and sufficient conditions under which such formulae do exist. Several formulae obtained by applying this method are considered and compared with well known formulae.</p
Accurate computation of multi-dimensional Riesz potentials
No full textThe paper discusses a fast method for computing the Riesz potentials in the framework of the method approximate approximations. By combining high-order cubature formulas with tensor product approximations, we derive an approximation of the potentials which is fast, accurate and provides approximation formulas of high order. The action of volume poten- tials on the basis functions introduced in the theory of approximate approximations allows one-dimensional integral representations with separable integrands, i.e. a product of functions depending on only one of the variables. Then a separated representation of the density, com- bined with a suitable quadrature rule, leads to a tensor product representation of the integral operator. Since only one-dimensional operations are used, the resulting method is effective also in the high-dimensional case
Teoria degli operatori intermedi e applicazioni: statica elastica con coefficienti discontinui, il problema degli spostamenti
No full text
Teoria degli operatori intermedi e applicazioni: statica elastica con coefficienti discontinui, il problema misto e i problemi di trasmissione
No full text
On BVPs for strongly elliptic systems with higher order boundary conditions
No full textWe consider BVPs for strongly elliptic systems of order 21 with the boundary conditions of order 1 +n, n>=0. By representing the solution by means of a simple layer potential of order n and by imposing the boundary conditions, we get a singular integral system which is of regular type if the boundary operator satisfies the Lopatinskii condition and which can be solved if suitable compatibility conditions are satisfied. An explicit formula for computing the index of the BVP is given
Numerical approximation of eigenvalues and of Green's operator for an elliptic boundary value problem
No full textThis paper is concerned with the Dirichlet problem for a second order linear elliptic equation with bounded and measurable coefficients. By using the theory of intermediate operators methods for the calculus of the Green operator and of the corresponding Green function are given. Numerical experiments are included. © Springer-Verlag 1998
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