A study of one dimensional nonlinear diffusion equations by Bernstein polynomial based differential quadrature method

The purpose of this work is to study numerical solutions of nonlinear diffusion equations such as Fisher's equation, Burgers' equation and modified Burgers' equation by applying Bernstein differential quadrature method (BDQM). These nonlinear diffusion equations occur in many applications of theoretical, engineering and environmental sciences. Therefore, finding numerical solutions of these equations is very important. In BDQM, Bernstein polynomials are used as base functions to find weighting coefficients of differential quadrature method. We have applied BDQM on eleven different test problems taken from the literature and the computed results confirm that BDQM is an efficient method for finding solution of nonlinear partial differential equations. It is found that BDQM produces very good results even at small number of grid points.