A regularization method for the elliptic equation with inhomogeneous source (Q2449030)

Summary: We consider a Cauchy problem for the elliptic equation with inhomogeneous source in a rectangular domain with Dirichlet boundary conditions at \(x=0\) and \(x=\pi\). The problem is ill-posed. The main aim of this paper is to introduce a regularization method and use it to solve the problem. Some sharp error estimates between the exact solution and its regularization approximation are given and a numerical example shows that the method works effectively.