FINITE-ELEMENT SOLUTION OF THE COUPLED-CHANNEL SCHRODINGER-EQUATION USING HIGH-ORDER ACCURACY APPROXIMATIONS

The finite element method (FEM) is applied to solve the bound state (S turm-Liouville) problem for systems of ordinary linear second-order di fferential equations. The convergence, accuracy and the range of appli cability of the high-order FEM approximations (up to tenth order) are studied systematically on the basis of numerical experiments for a wid e set of quantum-mechanical problems. The analytical and tabular forms of giving the coefficients of differential equations are considered. The Dirichlet and Neumann boundary conditions are discussed. It is sho wn that the use of the FEM high-order accuracy approximations consider ably increases the accuracy of the FE solutions with substantial reduc tion of the requirements on the computational resources. The results o f the FEM calculations for various quantum-mechanical problems dealing with different types of potentials used in atomic and molecular calcu lations (including the hydrogen atom in a homogeneous magnetic field) are shown to be well converged and highly accurate.