A Maple Implementation of the Finite Element Method for Solving Metastable State Problems for Systems of Second-Order Ordinary Differential Equations

We present a new algorithm for systems of second-order ordinary diff tial equations to calculate metastable states with complex eigenvalues of energy or to fi bound states with homogeneous boundary conditions depending on a spectral parameter. The boundary-value problems is discretized by means of the FEM using the Hermite interpolation polynomials with arbitrary multiplicity of the nodes, which preserves the continuity of derivatives of the desired solutions. For the solution of the relevant algebraic problems the Newton iteration scheme is implemented.