Use of modified Bernstein polynomials to solve KdV–Burgers equation numerically

Numerical solution of Korteweg-de Veries–Burgers (KdVB) equation is presented using modified Bernstein polynomials (B-polynomials). Over the spatial domain, B-polynomials are used to expand the desired solution requiring discretization with only the time variable. Galerkin method is used to determine the expansion coefficients to construct initial trial functions. We use fourth-order Runge–Kutta method to solve the system of equations for the time variable. The accuracy of the solutions is dependent on the size of the B-polynomial basis set. Numerical results obtained using this method are compared with existing analytical results. Excellent agreement is found between the exact solution and approximate solution obtained by this method.