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.
Highlights
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It will be shown that finding solutions from the Poisson and KleinGordon 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
First the partial derivatives equation is written as an integral equation φ(m, r)
Summary
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Eu, accumsan eleifend, sagitDuis eget orci sit amet orci t methods such as the method of finite differences [1,2,3,4]. Morbi auctor lorem non DjOusIt:o1.0.N4a2m36/lajcaums pli.b2e0r2o0,.8p8re1t2iu3m aAt,ulgo.bo2r5t,is2020 vitae, ultricies et, tellus. Tortor sed accumsan bibendum, erat ligula aliquet magna, vitae ornare odio metus a mi. We want to present a an alternative method to solve a Poisson equation under Neumann conditions using techniques of generalized inverse moment problem, independently of other commonly used existing methods: finite difference method, Galerkin method, among many others. One of them is the truncated expansion method [5] This method is to approximate (2) with the finite moments problem μi = gi(x)f (x)dx i = 1, 2, ..., n (4). In the case where the data μi are inaccurate the convergence theorems should be applied and error estimates for the regularized solution (p. 19 a 30 de [5])
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