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The probability approach to numerical solution of nonlinear parabolic equations
Author(s) -
Milstein G. N.
Publication year - 2002
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.10020
Subject(s) - probabilistic logic , mathematics , nonlinear system , convergence (economics) , partial differential equation , partial derivative , parabolic partial differential equation , probabilistic method , mathematical analysis , statistics , physics , quantum mechanics , economics , economic growth
A number of new layer methods for solving semilinear parabolic equations and reaction‐diffusion systems is derived by using probabilistic representations of their solutions. These methods exploit the ideas of weak sense numerical integration of stochastic differential equations. In spite of the probabilistic nature these methods are nevertheless deterministic. A convergence theorem is proved. Some numerical tests are presented. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 490–522, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10020