J Austral Math Soc Ser B 32 pp115--132, 1990.

Solution of a Schrödinger equation by iterative refinement

Rekha P. Kulkarni and Balmohan V. Limaye

Abstract

A simple eigenvalue and a corresponding wavefunction of a Schrödinger operator is initially approximated by the Galerkin method and by the iterated Galerkin method of Sloan. The initial approximation is iteratively refined by employing three schemes: the Rayleigh-Schrödinger scheme, the fixed point scheme and a modification of the fixed point scheme. Under suitable conditions, convergence of these schemes is established by considering error bounds. Numerical results indicate that the modified fixed point scheme along with Sloan's method performs better than the others.

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Authors

Rekha P. Kulkarni

Balmohan V. Limaye

Department of Mathematics, Indian Institute of Technology, Bombay 400 076, India.