Using the inverse Cauchy problem of the Laplace equation for wave propagation to implement a numerical regularization homotopy method.

In this paper, we introduce an approach via regularization and Homotopy way for resolving the inverse Cauchy problem of the Laplace of system partial differential equation which appears in the wave propagation for communication networks. We considered the method of Homotopy Perturbation Metheod (HPM) for solving the integral equations of the first kind named Fredholm. In order to formulate the Laplace equation into the first-kind integral equation (Fredholm) the Fourier series used. Then the discretization method used to reduce the integral equation into a linear operator equation for the first kind. It is clear that this kind of problem is callsified as an ill-posed and the direct way to solve it unacceptably. Tikhonov's regularization method with Homotopy Perturbation algorithm used for obtaing the approximation solution for the Laplace differential equation. Finally, the numerical example is proposed. [ABSTRACT FROM AUTHOR]