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A marker method for the solution of the damped Burgers' equation
Author(s) -
Lewandowski Jerome L. V.
Publication year - 2006
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.20088
Subject(s) - partial differential equation , mathematics , burgers' equation , partial derivative , first order partial differential equation , nonlinear system , function (biology) , mathematical analysis , field (mathematics) , separable partial differential equation , differential equation , ordinary differential equation , physics , pure mathematics , differential algebraic equation , quantum mechanics , evolutionary biology , biology
A new method for the solution of the damped Burgers' equation is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details. The marker method is applicable to a general class of nonlinear dispersive partial differential equations. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006