Jacobi spectral Galerkin method for the integrated forms of second-order differential equations (Q606838)

The authors introduce some ``integrated forms'' in order to solve by Galerkin method boundary value problems associated to one (1D) and two (2D) dimensional linear elliptic differential equations. The method is based on Jacobi polynomials. Reviewer's remark: It is not clear at all what is the exact mathematical significance of these ``integrated forms'' because the authors do not pay attention to usual formal aspects which could properly define them, i.e., domain of definition or the existence and uniqueness of the solutions. They claim that the Jacobi-Galerkin approximation associated to these ``integrated forms'' is a standard Galerkin one but do not prove this statement. Some numerical results obtained for 1D and 2D homogeneous Dirichlet problems associated to Poisson equation (and not Helmholtz!) seem to be fairly close to some other numerical results obtained using Chebyshev-tau or Galerkin and Legendre-Galerkin methods.