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A best approximation for the solution of one‐dimensional variable‐coefficient Burgers' equation
Author(s) -
Li Fuxiang,
Cui Minggen
Publication year - 2009
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.20428
Subject(s) - mathematics , mathematical analysis , variable (mathematics) , kernel (algebra) , space (punctuation) , bar (unit) , variable coefficient , burgers' equation , function (biology) , partial differential equation , combinatorics , physics , philosophy , linguistics , meteorology , biology , evolutionary biology
In this article, an iterative method for the approximate solution to one‐dimensional variable‐coefficient Burgers' equation is proposed in the reproducing kernel space W (3,2) . It is proved that the approximation w n ( x , t ) converges to the exact solution u ( x , t ) for any initial function w 0 ( x , t ) ε W (3,2) , and the approximate solution is the best approximation under a complete normal orthogonal system $ \{\bar{\psi}_{i}\}^{\infty}_{i=1} $ . Moreover the derivatives of w n ( x , t ) are also uniformly convergent to the derivatives of u ( x , t ).© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009