ON A CHEBYSHEV MATRIX OPERATOR METHOD FOR ORDINARY LINEAR-DIFFERENTIAL EQUATIONS WITH NONCONSTANT COEFFICIENTS

A spectral method based on the tau-method is developed to solve initial and boundary value problems. The usual problem of setting up the system of algebraic equations by sophisticated terms of the series coefficients is overcome by the use of operator matrices for derivation and multiplication with non-constant coefficients. The applicability is also given for eigenvalue problems as is demonstrated by the Orr-Sommerfeld equation.