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2004•Acta Scientiarum Naturalium Universitatis SunyatseniRequires access

MODIFIED LEGENDRE RATIONAL SPECTRAL METHOD FOR THE WHOLE LINE

Zhong-qingWang, Ben-yuGuo

Open publisher page 16 citations

Abstract

A mutually orthogonal system of rationalSome approximation results are establishedfunctions on the whole line is introduced.As an example of applications, a modified Legendre rational spectral scheme is given for the Dirac equation. Its numerical solution 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.

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What this paper is about

A mutually orthogonal system of rationalSome approximation results are establishedfunctions on the whole line is introduced.As an example of applications, a modified Legendre rational spectral scheme is given for the Dirac equation. Its numerical solution 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.

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OpenAlex reports 16 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A mutually orthogonal system of rationalSome approximation results are establishedfunctions on the whole line is introduced.As an example of applications, a modified Legendre rational spectral scheme is given for the Dirac equation. Its numerical solution 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 concepts: Legendre polynomials, Convergence (economics), Legendre wavelet, Mathematics, Scheme (mathematics), Applied mathematics, Line (geometry), Legendre transformation

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