Wm. Cao et Gq. He, RIGOROUS ANALYSIS OF AN IMPLICIT SPECTRAL METHOD FOR KDV EQUATION, Arabian journal for science and engineering, 22(2C), 1997, pp. 159-167
A Fourier spectral method in combination with the standard midpoint Eu
ler temporal discretization for the KdV equation is considered. The gl
obal existence and convergence of the numerical solution are investiga
ted rigorously. An iteration method for solving the nonlinear algebrai
c systems at each time level is also proposed, with its compression fa
ctor strictly estimated.