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 space W-2(D). It is proved the approximation wn(x, t) converges uniformly to the exact solution u(x, t) for any initial function w(0)(x, t) is an element of W-2(D) under trivial conditions, the derivatives of w(n)(x, t) are also convergent to the derivatives of u(x, t), and the approximate solution is the best approximation under the system {alpha(i)(x, t)}(i=1)(infinity). (C) 2014 Wiley Periodicals, Inc.