Gaussian-type quadrature rules for oscillatory integrand functions are presented. The weights and nodes depend on the frequency of the problem and they are constructed by following the exponential fitting theory. The error analysis proves that the exponentially fitted Gaussian rules are more accurate than the classical Gaussian rules when oscillatory functions are treated. The numerical approximation to Volterra integral equations with oscillatory solution through these formulas is presented. Some numerical tests are reported.
On quadrature formulas for oscillatory evolutionary problems
Angelamaria Cardone;Dajana Conte;Beatrice Paternoster
2018-01-01
Abstract
Gaussian-type quadrature rules for oscillatory integrand functions are presented. The weights and nodes depend on the frequency of the problem and they are constructed by following the exponential fitting theory. The error analysis proves that the exponentially fitted Gaussian rules are more accurate than the classical Gaussian rules when oscillatory functions are treated. The numerical approximation to Volterra integral equations with oscillatory solution through these formulas is presented. Some numerical tests are reported.File in questo prodotto:
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