An Efficient Numerical Method for a Spacewise Inverse Source Problem for a Multidimensional Parabolic Equation

In the present paper, a spacewise inverse source problemfor a linear multidimensional parabolic equation is considered. The main aimof the paper is to suggest an efficient numerical method based on finitedifferences for the considered problem. Furthermore, a couple of rigorousstability estimates are derived in terms of stability analysis of thesuggested numerical method. Finally, to exhibit the capability ofthe numerical method a comprehensive and illustrative numerical discussion,wherein the method is compared with another method in the literatureregarding the accuracy and computational cost, is given.