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Probabilistic viscosity algorithm for the scalar conservation law
Author(s) -
Korzeniowski Andrzej
Publication year - 1992
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690080304
Subject(s) - mathematics , scalar (mathematics) , conservation law , probabilistic logic , brownian motion , viscosity , representation (politics) , initial value problem , viscosity solution , mathematical analysis , algorithm , law , geometry , statistics , physics , quantum mechanics , politics , political science
We derive an algorithm for solving the initial value problem for u t = ½σ 2 u xx + f ( u ) u x . The approach is based on the representation of the solution to the above equation in the form of the functional of Brownian motion. For small σ we get the approximation for u t = f ( u ) u x . A comparison with the random choice method is illustrated by the numerical example.
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