Ritz-least squares method for finding a control parameter in a one-dimensional parabolic inverse problem

An inverse problem concerning a diffusion equation with source control parameter is considered. The approximation of the problem is based on the Ritz method with satisfier function. The Ritz method together with the least squares approximation (Ritz-least squares method) are utilized to reduce the inverse problem to the solution of algebraic equations. We extensively discuss the convergence of the method and finally present illustrative examples to demonstrate validity and applicability of the new technique.