The collocation method based on a generalized inverse multiquadric basis for bound-state problems

Xu Guang Hu, Tak San Ho, Herschel Rabitz

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

The generalized inverse multiquadric basis function (1 + c2∥x∥2)-β/2, where c > 0, β > d, and x ∈ ℝd, is introduced for numerically solving the bound-state Schrödinger equation. Combined with the collocation method, this basis function can yield accurate eigenvalues of highly excited vibrations, as demonstrated by using one-and two-dimensional potentials. In addition, the generalized inverse multiquadric basis function is as flexible and simple as the Gaussian basis. The multiquadric form does not call for semiclassically distributed grid points and specially scaled exponential parameters as required in the latter case to achieve high accuracy.

Original languageEnglish (US)
Pages (from-to)168-179
Number of pages12
JournalComputer Physics Communications
Volume113
Issue number2-3
DOIs
StatePublished - Oct 1998

All Science Journal Classification (ASJC) codes

  • Hardware and Architecture
  • Physics and Astronomy(all)

Keywords

  • Bound-state
  • Collocation method
  • Interpolation theory
  • Radial basis
  • Schödinger equation
  • Vibration energy level
  • Wavefunction

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