Accurate and efficient quadrature for volterra integral equations
| Autor: | Dwayne L Knirk |
|---|---|
| Rok vydání: | 1976 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Applied Mathematics Mathematical analysis Adaptive Simpson's method Richardson extrapolation Simpson's rule Volterra integral equation Integral equation Computer Science Applications Quadrature (mathematics) Computational Mathematics symbols.namesake Quadratic equation Modeling and Simulation symbols Linear approximation Mathematics |
| Zdroj: | Journal of Computational Physics. 21:371-399 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/0021-9991(76)90037-1 |
| Popis: | Four quadrature schemes have been tested and compared in considerable detail to determine their usefulness in the noniterative integral equation method for single channel quantum mechanical calculations. They are two forms of linear approximation (Trapezoidal rule) and two forms of quadratic approximation (Simpson's rule). Their implementation in this method is shown, a formal discussion of error propagation is given, and tests are performed to determine actual operating characteristics on various bound and scattering problems in different potentials. The quadratic schemes are generally superior to the linear ones in terms of accuracy and efficiency. The previous implementation of Simpson's rule is shown to possess an inherent instability which requires testing on each problem for which it is used to assure its reliability. The alternative quadratic approximation which we propose does not suffer this deficiency, but still enjoys the advantages of higher order. In addition, the new scheme obeys very well an h 4 Richardson extrapolation, whereas the old one does so rather poorly. |
| Databáze: | OpenAIRE |
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