Modified Legendre Rational Spectral Method for the Whole Line
Zhong Qing Wang 1, Ben Yu Guo 11 Department of Mathematics, Division of Computational Science of E-institute of Shanghai Universities,Shanghai Normal University, Shanghai 200234, China
A mutually orthogonal system of rational functions on the whole line is introduced. Some approximation results are established. As an example of applications, a modified Legendre rational spectral scheme is given for the Dirac equation. Its numerical solu- tion keeps the same conservation as the genuine solution. This feature not only leads to reasonable numerical simulation of nonlinear waves, but also simplifies the analysis. The convergence of the proposed scheme is proved. Numerical results demonstrate the efficiency of this new approach and coincide with the analysis well.
Key words: Modified Legendre rational approximation; The whole line; Dirac equation.