Numerical solution of the generalized Burger's equation via spectral/spline methods

In this paper we present a mixed spectral/spline approach to solve the generalized Burger's equation (GBE). The method is based on a Chebyshev spectral approximation in combination with 3-point spline collocation methods. The proposed method is accomplished by starting with Chebyshev spectral approximation for the highest-order derivative in the x-direction and generating approximations to the lower-order derivatives in the x-direction through successive integration of the highest-order derivative. The problem is then reduced to a system of ordinary differential equations in the t-direction, which will be treated by 3-point spline collocation methods.