Comparison of Numerical Methods for Solving the Second-Order Differential Equations of Molecular Scattering Theory

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The numerical solution of coupled, second-order differential equations is a fundamental problem in theoretical physics and chemistry. There are presently over 20 commonly used methods. Unbiased comparisons of the methods are difficult to make and few have been attempted. Here we report a comparison of 11 different methods applied to 3 different test problems. The test problems have been constructed to approximate chemical systems of current research interest and to be representative of the state of the art in inelastic molecular collisions. All calculations were done on the same computer and the attempt was made to do all calculations to ... continued below

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30 p.

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Thomas, L.D.; Alexander, M.H.; Johnson, B.R.; Lester Jr., W. A.; Light, J.C.; McLenithan, K.D. et al. July 1, 1980.

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Description

The numerical solution of coupled, second-order differential equations is a fundamental problem in theoretical physics and chemistry. There are presently over 20 commonly used methods. Unbiased comparisons of the methods are difficult to make and few have been attempted. Here we report a comparison of 11 different methods applied to 3 different test problems. The test problems have been constructed to approximate chemical systems of current research interest and to be representative of the state of the art in inelastic molecular collisions. All calculations were done on the same computer and the attempt was made to do all calculations to the same level of accuracy. The results of the initial tests indicated that an improved method might be obtained by using different methods in different integration regions. Such a hybrid program was developed and found to be at least 1.5 to 2.0 times faster than any individual method.

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30 p.

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  • Journal Name: Journal of Computational Physics; Journal Volume: 41; Journal Issue: 2

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  • Report No.: LBL-11233
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 994003
  • Archival Resource Key: ark:/67531/metadc1013908

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  • July 1, 1980

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  • Oct. 14, 2017, 8:36 a.m.

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  • Oct. 17, 2017, 6:10 p.m.

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Thomas, L.D.; Alexander, M.H.; Johnson, B.R.; Lester Jr., W. A.; Light, J.C.; McLenithan, K.D. et al. Comparison of Numerical Methods for Solving the Second-Order Differential Equations of Molecular Scattering Theory, article, July 1, 1980; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc1013908/: accessed October 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.