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Author(s):
T. Utsumi, J. Koga, T. Yabe, Y. Ogata, E. Matsunaga, T. Aoki and M. Sekine
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Title:
Basis Set Approach in the Constrained Interpolation Profile Method
Date of publication:
July 2003
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Key words:
CIP-BS method, CIP method, basis set, Schrodinger equation
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Abstract:
We propose a simple polynomial basis-set that is easily extendable to any desired higher-order accuracy. This method is based on the Constrained Interpolation Profile (CIP) method and the profile is chosen so that the subgrid scale solution approaches the real solution by the constraints from the spatial derivative of the original equation. Thus the solution even on the subgrid scale becomes consistent with the master equation. By increasing the order of the polynomial, this solution quickly converges.3rd and 5th order polynomials are tested on the one-dimensional Schrodinger equation and are proved to give solutions a few orders of magnitude higher in accuracy than conventional methods for lower-lying eigenstates.
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