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

Authors: Ben-Yu Guo and Jie Shen

Issue: Volume 50 (2001), Issue 1, 181-204

Abstract: A new set of modified Legendre rational functions which are mutually orthogonal in $L^2(0, +\infty)$ is introduced. Various projection and interpolation results using the modified Legendre rational functions are established. These results form the mathematical foundation of related spectral and pseudospectral 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 numerical 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.