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