Numerical solution of the inverse problem of reconstructing a distributed right-hand side of a parabolic equation

Abstract

We consider the inverse problem of reconstructing the right-hand side (RHS) of a parabolic equation using a solution specified at internal points. Dependence of the RHS on time is the unknown variable. Such a problem is typical of heat transfer and hydrogeology. Various approaches to solution of this problem are discussed. We present a numerical algorithm based on the transition to the problem of the loaded parabolic equation. For solving this nonclassical problem, we employ a special numerical method similar to the bordering method. Such a general approach can be used both for parabolic equations that are one-dimensional in space and for multidimensional ones.