Artículos de revistas
On the numerical solution of the linear and nonlinear Poisson equations seen as bi-dimensional inverse moment problems
Pintarelli, María Beatriz; Vericat, Fernando; On the numerical solution of the linear and nonlinear Poisson equations seen as bi-dimensional inverse moment problems; Taylor & Francis; Journal of Interdisciplinary Mathematics; 19; 5-6; 12-2016; 927-944
Pintarelli, María Beatriz
The numerical solution of the bi-dimensional nonlinear Poisson equations under Cauchy boundary conditions is considered. Using Green identity we show that this problem is equivalent to solve a bi-dimensional Fredholm integral equation of the first kind which can in turn be handled as a bi-dimensional generalized inverse moment problem. In the particular linear case the Helmholtz PDE is recovered and, within our scheme, the problem reduces to a bi-dimensional Hausdorff moment problem. In all the cases we find approximated solutions for the associated finite moment problems and bounds for the corresponding errors.