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Radial quadrature for multiexponential integrands.

Peter M W Gill1, Siu-Hung Chien

  • 1School of Chemistry, University of Nottingham, Nottingham NG7 2RD, United Kingdom.

Journal of Computational Chemistry
|April 1, 2003
PubMed
Summary

A new Gaussian quadrature method is presented for radial integrals. This method accurately evaluates integrals with multiexponential behavior, offering an alternative to existing techniques.

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Area of Science:

  • Numerical Analysis
  • Computational Physics
  • Quantum Chemistry

Background:

  • Radial integrals are crucial in various scientific fields.
  • Existing numerical methods may struggle with certain integrand behaviors, like multiexponential functions.

Purpose of the Study:

  • To introduce a novel Gaussian quadrature scheme for evaluating radial integrals.
  • To provide an accurate method for integrands with multiexponential behavior.

Main Methods:

  • Developed a Gaussian quadrature based on orthogonal polynomials.
  • The weight function used is ln(2)x on the interval [0, 1].
  • The quadrature is exact for integrands that are linear combinations of exponential functions.

Main Results:

  • The proposed Gaussian quadrature is suitable for radial integral evaluation.
  • The method demonstrates accuracy for integrands with multiexponential characteristics.
  • It serves as a valuable alternative to current numerical approaches.

Conclusions:

  • The new Gaussian quadrature offers an efficient and accurate solution for specific radial integral evaluations.
  • This method is particularly advantageous for problems involving multiexponential functions.

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