A best approximation for the solution of one‐dimensional variable‐coefficient Burgers' equation

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