Recursive construction of particular solutions to nonhomogeneous linear partial differential equations of elliptic type (Q1186914)

The authors have previously considered the numerical solution of elliptic equations in terms of harmonic polynomials and a least squares collocation procedure, matching the boundary conditions. In this paper, a recursive method is designed and tested numerically for the more general case with a right hand side which can be approximated well by polynomials. Approximate particular solutions are computed by recursively determining the coefficients of polynomials which represent the solution.