Inverse Multiquadratic Functions as the Basis for the Rectangular Collocation Method to Solve the Vibrational Schrödinger Equation
| Autor: | Sergei Manzhos, Aditya Kamath |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
General Mathematics
Gaussian Inverse Schrödinger equation rectangular matrix Basis function 010402 general chemistry 01 natural sciences Square (algebra) symbols.namesake Collocation method 0103 physical sciences Computer Science (miscellaneous) Applied mathematics inverse multiquadratic function Engineering (miscellaneous) Mathematics collocation Collocation 010304 chemical physics Basis (linear algebra) lcsh:Mathematics vibrational spectrum Function (mathematics) lcsh:QA1-939 0104 chemical sciences symbols |
| Zdroj: | Mathematics, Vol 6, Iss 11, p 253 (2018) Mathematics Volume 6 Issue 11 |
| ISSN: | 2227-7390 |
| DOI: | 10.3390/math6110253 |
| Popis: | We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrö dinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions) is compared to that obtained using Gaussian basis functions when using different numbers of width-optimized IMQ functions. The effects of the ratio of the number of collocation points to the number of basis functions and of the choice of the IMQ exponent are studied. We show that the IMQ basis can be used with parameters where the IMQ function is not integrable. We find that the quality of the spectrum with IMQ basis functions is somewhat lower that that with a Gaussian basis when the basis size is large, and for a range of IMQ exponents. The IMQ functions are however, advantageous when a small number of functions is used or with a small number of collocation points (e.g., when using square collocation). |
| Databáze: | OpenAIRE |
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