On spectral approximations using modified Legendre rational functions: Application to the Korteweg-de Vries equation on the half line

A new set of modified Legendre rational functions which are mutually orthog onal in L-2 (0, + infinity) is introduced. Various projection and interpola tion results using the modified Legendre rational functions are established . These results form the mathematical foundation of related spectral and ps eudospectral methods for solving partial differential equations on the half line. A spectral scheme using the modified Legendre rational functions for the Korteweg-de Vries equation on the half line is investigated. The numer ical solution of the scheme is shown to possess the essential conservation properties satisfied by the solution of the Korteweg-de Vries equation. The spectral convergence of the proposed scheme is established.