کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4639471 1632051 2013 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A unified approach with spectral convergence for the evaluation of hypersingular and supersingular integrals with a periodic kernel
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
A unified approach with spectral convergence for the evaluation of hypersingular and supersingular integrals with a periodic kernel
چکیده انگلیسی

In this paper, a general class of methods is proposed for the evaluation of hypesingular/supersingular integrals with a periodic integrand, of singularity higher than or equal to 2. The method is based on regularizing the singular integrals into proper regular integrals when we can apply the classical trapezoidal rule. Error analysis is presented for hypesingular/supersingular integrals with a singularity of order p+1p+1, where pp is a positive integer. We prove that the convergence rate of the method is of O(lnn/nk+α)O(lnn/nk+α) if the integrand uu satisfies u∈C̃k+p,α[0,2π] (for any positive integer kk), with exponential convergence rate if the integrand uu is analytic. Several numerical examples are provided to support the theoretical error analysis.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 239, 1 February 2013, Pages 322–332
نویسندگان
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