Partial Differential Equations as Three-Dimensional Inverse Problem of Moments

Abstract

We considerer partial differential equations of second order, for example the Klein-Gordon equation, the Poisson equation, on a region E= (a1, b1)x(a2, b2)x(a3, b3). We will see that with a common procedure in all cases, we can write the equation in partial derivatives as an Fredholm integral equation of first kind and will solve this latter with the techniques of inverse problem moments. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on problem of moments.