کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4627236 1631804 2015 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems
ترجمه فارسی عنوان
مقایسه عملکرد روشهای معکوس عددی برای تبدیل انتگرال لاپلاس و هانکل در مشکلات مهندسی
کلمات کلیدی
تبدیل لاپلاس، تبدیل هانکل، معکوس عددی، انحراف تبدیل مشترک، روش های شتاب
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی

Different methods for the numerical evaluations of the inverse Laplace and inverse of joint Laplace–Hankel integral transforms are applied to solve a wide range of initial-boundary value problems often arising in engineering and applied mathematics. The aim of the paper is to present a performance comparison among different numerical methods when they are applied to transformed functions related to actual engineering problems found in the literature. Most of our selected test functions have been found in the solution of boundary value problems of applied mechanics such as those related to transient responses of isotropic and transversely isotropic half-space to concentrated impulse or those related to viscoelastic wave motion in layered media. These classes of test functions are frequently encountered in similar problems such as those in boundary element or boundary integral equations, theoretical seismology, soil–structure-interaction in time domain and so on. Therefore, their behavior with different numerical inversion algorithms could make a useful guide to a precise choice of more suitable inversion method to be used in similar problems. Some different methods are also investigated in detail and compared for the inversion of the joint Hankel–Laplace transforms, where more sophisticated integrand functions are encountered. It is shown that Durbin, Crump, D’Amore, Fixed-Talbot, Gaver–Whyn–Rho (GWR), and Direct Integration methods have excellent performance and produce good results when applied to the same problems. On the contrary, Gaver–Stehfest and Piessens methods furnish results not very reliable for almost all classes of transformed functions and they seem good only for “simple” transformed functions. Particularly the performance of GWR algorithm is very good even for transformed functions with infinite number of singularities, where the other methods fail. In addition, in case of double integral transforms, only the Fixed-Talbot, Durbin and Weeks methods are recommended.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 250, 1 January 2015, Pages 759–775
نویسندگان
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