期刊
MOLECULAR PHYSICS
卷 107, 期 13, 页码 1339-1348出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/00268970902873554
关键词
high order finite element method; h-adaptive method; Lobatto basis functions; radial Schrodinger equation
The h-adaptive, high order finite element method is applied to solve a second order one dimension eigenvalue problem. The finite element formulation for the Lobatto basis is given, for which basis functions of arbitrary order can be constructed. The adaptive algorithm is simple, yet very efficient and straightforward to implement. The algorithm is based on the observation that the expansion coefficients of Lobatto basis functions decay rapidly. It allows evaluating the smallest eigenvalues simultaneously with the comparable accuracy for all eigenvalues. The presented algorithm is applied to solve the radial Schrodinger equation with the Coulomb and the Woods-Saxon potentials. For both potentials the convergence rate is presented. After seven adaptive iterations nine-digit accuracy was obtained.
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