This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions. Firstly, the problem is reduced to an equivalent problem which is easy to handle using variational iteration method. Secondly, variational iteration method is used to solve the reduced problem. Using this method a rapid convergent sequence can be produced which tends to the exact solution of the problem. Furthermore, variational iteration method does not require the discretization of the problem. Two numerical examples are presented to illustrate the strength of the method.
Xiuming Li. Suping Qian. "Numerical Solution of the Inverse Problem of Determining an Unknown Source Term in a Heat Equation." J. Appl. Math. 2012 1 - 9, 2012. https://doi.org/10.1155/2012/390876