On the Numerical Solution to an Inverse Problem of Recovering a Source of Special Type in a Parabolic Equation

We consider an inverse problem of recovering a source of special type in a parabolic equation under initial and boundary conditions. The specificity of the problem is that the identifiable parameters depend only on a time variable and are factors of coefficient of the free term of the right-hand side of the equation. We propose a numerical method to solve the problem, based on the method of lines and a special representation of the solution. The method does not require any iterative procedures to be generated. The results of numerical experiments conducted for test problems are provided.