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Numerical solution of one‐dimensional Burgers' equation
Author(s) -
Li FuXiang,
Fei ZhaoFu,
Han Jing,
Wei Jia
Publication year - 2015
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.21945
Subject(s) - mathematics , kernel (algebra) , mathematical analysis , burgers' equation , partial differential equation , space (punctuation) , function (biology) , class (philosophy) , pure mathematics , linguistics , philosophy , evolutionary biology , artificial intelligence , computer science , biology
In this article, an iterative method for the approximate solution of a class of Burgers' equation is obtained in reproducing kernel spaceW 2 ( D ) . It is proved the approximationw n ( x , t ) converges uniformly to the exact solution u ( x , t ) for any initial functionw 0 ( x , t ) ∈ W 2 ( D ) under trivial conditions, the derivatives ofw n ( x , t ) are also convergent to the derivatives of u ( x , t ), and the approximate solution is the best approximation under the system{ α i ( x , t ) } i = 1 ∞ . © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1251–1264, 2015