A stable marching difference scheme for an ill-posed Cauchy problem for the three-dimensional Laplace equation

Ill-posed problems for PDEs (35R25) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)