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 W2(D). It is proved the approximation wn(x,t) converges uniformly to the exact solution u(x, t) for any initial function w0(x,t)∈W2(D) under trivial conditions, the derivatives of wn(x,t) are also convergent to the derivatives of u(x, t), and the approximate solution is the best approximation under the system {αi(x,t)}i=1∞. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1251–1264, 2015