On a generalized basis for solving the one dimensional transport equation: Theory

Abstract: The most general basis for approximating the transport equation has been studied. The application of the Gram–Schmidt procedure has been shown to unify the complete class of functions (polynomial type or non-polynomial type), applicable to this equation. The completeness of the series of functions is proved. A generalized version of the Fick''s law is introduced. It is shown that the spectrum of the transport equation obtained by this method agrees with the conventional methods of obtaining the spectrum. [Copyright &y& Elsevier]