SEARCH

SEARCH BY CITATION

Keywords:

  • spectral collocation methods;
  • high-order ordinary differential equations;
  • multiple boundary conditions;
  • integrated basis-functions

Abstract

This paper reports a new Chebyshev spectral collocation method for directly solving high-order ordinary differential equations (ODEs). The construction of the Chebyshev approximations is based on integration rather than conventional differentiation. This use of integration allows the multiple boundary conditions to be incorporated more efficiently. Numerical results show that the proposed formulation significantly improves the conditioning of the system and yields more accurate results and faster convergence rates than conventional formulations. Copyright © 2005 John Wiley & Sons, Ltd.