کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8902108 | 1631956 | 2018 | 34 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Error analysis of the Wiener-Askey polynomial chaos with hyperbolic cross approximation and its application to differential equations with random input
ترجمه فارسی عنوان
تجزیه و تحلیل خطا هرج و مرج چندجملهای وینر-اشکی با تقریب متقابل هیپربولیک و کاربرد آن برای معادلات دیفرانسیلی با ورودی تصادفی
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
چکیده انگلیسی
It is well-known that sparse grid algorithm has been widely accepted as an efficient tool to overcome the “curse of dimensionality” in some degree. In this note, we give the error estimate of hyperbolic cross (HC) approximations with all sorts of Askey polynomials. These polynomials are useful in generalized polynomial chaos (gPC) in the field of uncertainty quantification. The exponential convergences in both regular and optimized HC approximations have been shown under the condition that the random variable depends on the random inputs smoothly in some degree. Moreover, we apply gPC to numerically solve the ordinary differential equations with slightly higher dimensional random inputs. Both regular and optimized HC have been investigated with Laguerre-chaos, Charlier-chaos and Hermite-chaos in the numerical experiment. The discussion of the connection between the standard ANOVA approximation and Galerkin approximation is in the appendix.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 335, June 2018, Pages 242-269
Journal: Journal of Computational and Applied Mathematics - Volume 335, June 2018, Pages 242-269
نویسندگان
Xue Luo,