Time and space splitting techniques are applied to the Burgers' equation and the modified Burgers' equation, and then the quintic B-spline collocation procedure is employed to approximate the resulting systems. Some numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method. Comparisons with both analytical solutions and some published numerical results are done in computational section. (C) 2007 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.