Solution of Partial Derivative Equations of Poisson and Klein-Gordon with Neumann Conditions as a Generalized Problem of Two-Dimensional Moments

Maria B. Pintarelli^1,2

¹Department of Basic Sciences, Faculty of Engineering, National University of La Plata, La Plata, Argentina.
²Mathematics Department, Faculty of Exact Sciences, National University of La Plata, La Plata, Argentina.

DOI: 10.4236/jamp.2020.88123                

Abstract

It will be shown that finding solutions from the Poisson and Klein-Gordon equations under Neumann conditions are equivalent to solving an integral equation, which can be treated as a generalized two-dimensional moment problem over a domain that is considered rectangular. The method consists to solve the integral equation numerically using the two-dimensional inverse moments problem techniques. We illustrate the different cases with examples.

Keywords

Equation in Poisson Partial Derivatives, Klein-Gordon Equation, Integral Equations, Generalized Moment Problem

Conflicts of Interest

The author declares no conflicts of interest regarding the publication of this paper.

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