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

J. L. Casti und M. Scott (Editoren)
H. M. El-Hawary und Essam O. Abdel-Rahman
In: Applied Mathematics and Computation (Nov. 2005), 170:1(267-279)
 

Abstract

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.

Stichwörter: generalized Burger’s equation (GBE), spline collocation and Chebyshev approximation

Bibtex

@ARTICLE{abdel-rahman-2005-numerical,
     author = {El-Hawary, H. M. and Abdel-Rahman, Essam O.},
     editor = {Casti, J. L. and Scott, M.},
      pages = {267--279},
      title = {Numerical solution of the generalized Burger's equation via spectral/spline methods},
    journal = {Applied Mathematics and Computation},
     volume = {170},
     number = {1},
       year = {2005},
      month = nov,
  publisher = {Elsevier},
   keywords = {generalized Burger’s equation (GBE), spline collocation and Chebyshev approximation},
   abstract = {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.},
       issn = {0096-3003}
}