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A Hermite collocation method for approximating a class of highly oscillatory integral equations using new Gaussian radial basis functions
Calcolo ( IF 1.7 ) Pub Date : 2021-04-28 , DOI: 10.1007/s10092-021-00416-7
H. Ranjbar , F. Ghoreishi

In this paper, we investigate the oscillation properties of solutions of a class of highly oscillatory Volterra integral equations and develop a Hermite collocation method to approximate the solution of these equations. We begin our analysis by obtaining an asymptotic expansion for the solution of these equations using their resolvent representation. We then introduce a new Gaussian radial basis function interpolation to provide a numerical solution for these equations. The convergence analysis of the proposed method is also studied, which shows that increasing the number of collocation points or the number of mesh points controls the impact of the oscillation parameter in the whole error. Some numerical examples are presented to show the accuracy of the proposed scheme.



中文翻译:

一种使用新的高斯径向基函数逼近一类高振荡积分方程的Hermite配置方法

在本文中,我们研究了一类高度振荡的Volterra积分方程解的振动性质,并开发了一种Hermite配置方法来近似这些方程的解。我们通过使用它们的分解表示形式获得这些方程式解的渐近展开式,开始进行分析。然后,我们引入一种新的高斯径向基函数插值,以为这些方程式提供数值解。对所提方法的收敛性分析也进行了研究,结果表明,增加并置点数或网格点数可以控制振荡参数对整个误差的影响。给出了一些数值例子来说明所提方案的准确性。

更新日期:2021-04-29
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