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 initia l and boundary value problems. The usual problem of setting up the sys tem of algebraic equations by sophisticated terms of the series coeffi cients is overcome by the use of operator matrices for derivation and multiplication with non-constant coefficients. The applicability is al so given for eigenvalue problems as is demonstrated by the Orr-Sommerf eld equation.