Numerical solution of one‐dimensional Burgers' equation

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