Homotopy Algorithm Solving Inverse Source Problem For A Kind Of Parabolic PDE With Dirac Function

Inverse problem in parabolic equation is mainly discussed in heat conduction modeling and contaminant transport modeling, while the ho-motopy method is a global convergent method with a lot of application. In this article, we applied the homotopy method to the inverse problem in parabolic equation with Dirac function, focused on the problem of de-tecting the source intensity and position. The algorithm and numerical experiments are supplied to show the benefit of this method.Consider a parabolic equation with Neumann boundary condition: If we know the source intensity function Cs(t) and source position p,the equation can be solved,we call solving the equation as’Direct Problem’.If we do not know the Cs(t) and p,then if we have some observation wells that provide us the following data:The Inverse Problem we will discuss is to calculate the source intensity Cs(t) and position p with the observation data. To calculate this problem,considering the Dirac function,we use the Fouri-er spectral method,denoted as C*(x, t).Now we can give a non-linear op-erator equation In the abstract,calculating Cs(t) and p equal to solving the nonlinear operator equation To solve the equation,we use the homotopy method.For improving the stability of the method,we introduce the regularization method and com-pare with the Newton iteration method.We can see the advantages like stability,a wide range of convergence and efficient of the method in the numerical examples.