Numerical Treatment of Some Pdes : via Spectral and Spline Collocation Methods

In this book we present a mixed spectral/spline approach to solve the generalized Burger's equation. 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.