کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5776676 | 1632154 | 2017 | 40 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Order reduction phenomenon for general linear methods
ترجمه فارسی عنوان
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات محاسباتی
چکیده انگلیسی
The order reduction phenomenon for general linear methods (GLMs) for stiff differential equations is investigated. It turns out that, similarly as for standard Runge-Kutta methods, the effective order of convergence for a large class of GLMs applied to stiff differential systems, is equal to the stage order of the method. In particular, it is demonstrated that the global error âe[n]â of GLMs of order p and stage order q applied to the Prothero-Robinson test problem yâ²(t)=λ(y(t)âÏ(t))+Ïâ²(t), tâ[t0,T], y(t0)=Ï(t0), is O(hq)+O(hp) as hâ0 and hλâââ. Moreover, for GLMs with Runge-Kutta stability which are A(0)-stable and for which the stability function R(z) of the underlying Runge-Kutta methods, (i.e., the corresponding RK methods which have the same absolute stability properties as the GLMs), is such that R(â)â 1, the global error satisfies âe[n]â=O(hq+1)+O(hp) as hâ0 and hλâââ. These results are confirmed by numerical experiments.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 119, September 2017, Pages 94-114
Journal: Applied Numerical Mathematics - Volume 119, September 2017, Pages 94-114
نویسندگان
MichaÅ BraÅ, Angelamaria Cardone, ZdzisÅaw Jackiewicz, Bruno Welfert,