On the numerical solution of the linear and nonlinear Poisson equations seen as bi-dimensional inverse moment problems. Issue 5 (1st November 2016)

• Record Type: Journal Article
• Authors: Pintarelli, María B.; Vericat, Fernando
• Is Part Of: Journal of interdisciplinary mathematics. Volume 19:Issue 5/6(2016)
• Page Start: 927
• Page End: 944
• Publication Date: 2016-11-01
• Subjects: Nonlinear Poisson equation -- Fredholm integral equations -- Hausdorff moment problem -- generalized moment problem; 44A60 -- 65J22; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.1080/09720502.2014.916845
• Languages: English
• ISSNs: 0972-0502

Abstract

Abstract: 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.