An integral Chebyshev expansion method for boundary-value problems of O.D.E. type

AbstractA Chebyshev expansion method for the solution of boundary-value problems of O.D.E. type is presented. The method employs the pseudospectral (collocation) approximation and generates approximations to the lower order derivatives of the function through successive integrations of the Chebyshev polynomial approximation to the highest order derivative. The method is easier to implement than spectral methods employing the Galerkin and tau approximations and yields results of comparable accuracy to these methods, with reduced computing requirements. Applications to the linear stability problems for plane Poiseuille and the Blasius boundary layer flows are presented