کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4641437 | 1341309 | 2008 | 31 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An implicit finite volume scheme for a scalar hyperbolic problem with measure data related to piecewise deterministic Markov processes
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
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چکیده انگلیسی
We are interested here in the numerical approximation of a family of probability measures, solution of the Chapman-Kolmogorov equation associated to some non-diffusion Markov process with uncountable state space. Such an equation contains a transport term and another term, which implies redistribution of the probability mass on the whole space. An implicit finite volume scheme is proposed, which is intermediate between an upstream weighting scheme and a modified Lax-Friedrichs one. Due to the seemingly unusual probability framework, a new weak bounded variation inequality had to be developed, in order to prove the convergence of the discretised transport term. Such an inequality may be used in other contexts, such as for the study of finite volume approximations of scalar linear or nonlinear hyperbolic equations with initial data in L1. Also, due to the redistribution term, the tightness of the family of approximate probability measures had to be proven. Numerical examples are provided, showing the efficiency of the implicit finite volume scheme and its potentiality to be helpful in an industrial reliability context.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 222, Issue 2, 15 December 2008, Pages 293-323
Journal: Journal of Computational and Applied Mathematics - Volume 222, Issue 2, 15 December 2008, Pages 293-323
نویسندگان
Robert Eymard, Sophie Mercier, Alain Prignet,