کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1140391 956724 2010 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Monte Carlo solution of Cauchy problem for a nonlinear parabolic equation
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی کنترل و سیستم های مهندسی
پیش نمایش صفحه اول مقاله
Monte Carlo solution of Cauchy problem for a nonlinear parabolic equation
چکیده انگلیسی

In this paper we consider the Monte Carlo solution of the Cauchy problem for a nonlinear parabolic equation. Using the fundamental solution of the heat equation, we obtain a nonlinear integral equation with solution the same as the original partial differential equation. On the basis of this integral representation, we construct a probabilistic representation of the solution to our original Cauchy problem. This representation is based on a branching stochastic process that allows one to directly sample the solution to the full nonlinear problem. Along a trajectory of these branching stochastic processes we build an unbiased estimator for the solution of original Cauchy problem. We then provide results of numerical experiments to validate the numerical method and the underlying stochastic representation.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Mathematics and Computers in Simulation - Volume 80, Issue 6, February 2010, Pages 1118–1123
نویسندگان
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