Open AccessSolution of an Integro-differential Equation with Dirichlet Conditions using Techniques of the Inverse Moments Problem
Author(s) -
María Beatriz Pintarelli
Publication year - 2021
Publication title -
journal of mathematical sciences and computational mathematics
Language(s) - English
Resource type - Journals
eISSN - 2688-8300
pISSN - 2644-3368
DOI - 10.15864/jmscm.3101
Subject(s) - mathematics , integro differential equation , inverse problem , mathematical analysis , moment problem , partial differential equation , moment (physics) , integral equation , inverse , differential equation , dirichlet problem , hyperbolic partial differential equation , first order partial differential equation , boundary value problem , physics , geometry , statistics , classical mechanics , principle of maximum entropy
It will be shown that finding solutions from some integro-differential equation under Dirichlet conditions is equivalent to solving an integral equation, which can be treated as a generalized two-dimensional moment problem over a domain E = {( x , t ), 0 > x > L ; t > 0}. We will see that an approximate solution of the equation integro-differential can be found using the techniques of generalized inverse moments problem and bounds for the error of the estimated solution. First the problem is reduced to solving a hyperbolic or parabolic partial derivative equation considering the unknown source. The method consists of two steps. In each one an integral equation is solved numerically using the two-dimensional inverse moment problem techniques. We illustrate the different cases with examples.