کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
472081 698688 2015 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Explicit hard bounding functions for boundary value problems for elliptic partial differential equations
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر علوم کامپیوتر (عمومی)
پیش نمایش صفحه اول مقاله
Explicit hard bounding functions for boundary value problems for elliptic partial differential equations
چکیده انگلیسی

We obtain tight super- and sub-solutions, or hard bounding functions for the probabilistic representation of the solution, to the boundary value problem for second-order elliptic partial differential equations in an explicit polynomial form. Unlike accurate approximate solutions by the existing discretization-based methods, our hard bounding polynomial functions act as pointwise 100% confidence intervals within which the solution is guaranteed to exist. Our methodology can deal with a wide range of boundary conditions even of fully mixed type with Dirichlet, Neumann and Robin components, without increasing the complexity. The quality of hard bounds can be improved by introducing piecewise polynomial functions and domain decomposition. Convergence of hard bounding functions is proved under technical conditions. Numerical results are presented throughout the paper to support our theoretical developments and to illustrate the effectiveness of our methodology.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computers & Mathematics with Applications - Volume 70, Issue 12, December 2015, Pages 2822–2837
نویسندگان
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