Numerical solution of KdV equation using modified Bernstein polynomials Dambaru D. Bhatta a, * , Muhammad I. Bhatti b a Department of Mathematics, The University of Texas-Pan American, Edinburg, TX 78541-2999, USA b Department of Physics and Geology, The University of Texas-Pan American, Edinburg, TX 78541-2999, USA Abstract Here we present an algorithm for approximating numerical solution of Korteweg–de Vries (KdV) equation in a modified B-polynomial basis. A set of continuous polynomi- als over the spatial domain is used to expand the desired solution requiring discretiza- tion with only the time variable. Galerkin method is used to determine the expansion coefficients to construct initial trial functions. For the time variable, the system of equa- tions is solved using fourth-order Runge–Kutta method. The accuracy of the solutions is dependent on the size of the B-polynomial basis set. We have presented our numerical result with an exact analytical result. Excellent agreement is found between exact and approximate solutions. This procedure has a potential to be used in more complex system of differential equations where no exact solution is available. Ó 2005 Elsevier Inc. All rights reserved. Keywords: Korteweg–de Vries equation; B-polynomials; GalerkinÕs method; Runge–Kutta method 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.05.049 * Corresponding author. E-mail addresses: bhattad@utpa.edu (D.D. Bhatta), bhatti@utpa.edu (M.I. Bhatti). Applied Mathematics and Computation 174 (2006) 1255–1268 www.elsevier.com/locate/amc