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Knabner, P. and Angerman, L. (2006) Numerical Methods for Elliptic and Parabolic Partial Differential Equations. Springer, Berlin.

has been cited by the following article:

• TITLE: Parabolic Partial Differential Equations with Border Conditions of Dirichlet as Inverse Moments Problem

  AUTHORS: Mara B. Pintarelli

  KEYWORDS: Parabolic PDEs, Integral Equations, Generalized Moment Problem

  JOURNAL NAME: Applied Mathematics, Vol.8 No.1, January 18, 2017

  ABSTRACT: We considerer parabolic partial differential equations: under the conditions , on a region . We will see that an approximate solution can be found using the techniques of generalized inverse moments problem and also bounds for the error of estimated solution. First we transform the parabolic partial differential equation to the integral equation . Using the inverse moments problem techniques we obtain an approximate solution of . Then we find a numerical approximation of when solving the integral equation , because solving the previous integral equation is equivalent to solving the equation .