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- Hassan Majidian
- Numerical Algorithms
- 2017

The problem of computing oscillatory integrals with general oscillators is considered. We employ a Filon-type method, where the interpolation basis functions are chosen in such a way that the moments are in terms of elementary functions and the oscillator only. This allows us to evaluate the moments rapidly and easily without needing to engage… (More)

Anew approach for creating stable quadrature rules with preassigned points is proposed. The idea is to approximate a known stable quadrature rule by a local interpolation at the preassigned points. The construction cost of the method does not grow as the number of the preassigned points increases. The accuracy of the rule depends only on the accuracy of the… (More)

- Hassan Majidian
- 2012

In highly oscillatory integrals, the integrand fw(x) oscillates rapidly with a frequency ω. For very high values of ω, numerical evaluation of such integrals by Gaussian quadrature rules can be of very low accuracy. In such problems which have many applications in mathematical physics, it is important to devise algorithms with errors which decrease as fast… (More)

- Hassan Majidian
- Numerical Algorithms
- 2012

A numerical steepest descent method, based on the Laguerre quadrature rule, is developed for integration of one-dimensional highly oscillatory functions on [0, ∞ ) of a general class. It is shown that if the integrand is analytic, then in the absence of stationary points, the method is rapidly convergent. The method is extended to the case when there are a… (More)

- Hassan Majidian
- Numerical Algorithms
- 2013

A modified Euler’s method applied on a graded mesh is considered for numerical solution of a class of Volterra integral equations with weakly singular kernel which depends on a parameter μ > 0. It is shown that the convergence rate of the considered method is higher than those of earlier ones for the case when μ ≤ 1. The convergence rate is also obtained in… (More)

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