Finite difference methods for boundary value problems involving PDEs, high accuracy, Iterative numerical methods for linear systems, numerical examples, Multigrid methods; domain decomposition for boundary value problems involving PDEs, three-dimensional biharmonic equation, Error bounds for boundary value problems involving PDEs, finite differences, Numerical computation of matrix norms, conditioning, scaling, compact approximations, Symbolic computation and algebraic computation, Biharmonic and polyharmonic equations and functions in higher dimensions, Krylov subspace method, Boundary value problems for higher-order elliptic equations, preconditioning, Packaged methods for numerical algorithms, multigrid method, symbolic algebra package