IFLYSIB 05383
INSTITUTO DE FISICA DE LIQUIDOS Y SISTEMAS BIOLOGICOS
Unidad Ejecutora - UE
artículos
Título:
On the numerical solution of the linear and nonlinear Poisson equations seen as bi-dimensional inverse moment problems
Autor/es:
VERICAT, FERNANDO; PINTARELLI, MARÍA B.
Revista:
JOURNAL OF INTERDISCIPLINARY MATHEMATICS
Editorial:
Taylor & Francis
Referencias:
Lugar: NEW DELHI; Año: 2016 vol. 19 p. 927 - 944
ISSN:
0972-0502
Resumen:
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.
