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Solution of a Schrödinger equation by iterative refinement

Published online by Cambridge University Press:  17 February 2009

Rekha P. Kulkarni and
Balmohan V. Limaye
Balmohan V. Limaye
Affiliation:
Department of Mathematics, Indian Institute of Technology, Bombay 400 076, India.
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Abstract

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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.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 32 , Issue 1 , July 1990, pp. 115 - 131
Copyright
Copyright © Australian Mathematical Society 1990

References

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