Second order Jacobi approximation with applications to fourth-order differential equations

Authors:
Ben-yu Guo;Zhong-qing Wang;Zheng-su Wan;Delin Chu
Affiliations:
Department of Mathematics, Division of Computational Science of E-Institute of Shanghai Universities, Shanghai Normal University, Shanghai, China;Department of Mathematics, Division of Computational Science of E-Institute of Shanghai Universities, Shanghai Normal University, Shanghai, China;Department of Mathematics, Shanghai University, Shanghai, China;Department of Mathematics, National University of Singapore, Singapore, Singapore
Venue:
Applied Numerical Mathematics
Year:
2005

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Abstract

Second order Jacobi approximation in non-uniformly weighted Sobolev space is investigated. Some approximation results on various orthogonal projections are established, which serve as the mathematical foundation of Jacobi spectral methods for differential equations of fourth order. Jacobi spectral schemes are provided for several model problems. The convergence is proved. Numerical results agree well with theoretical analysis and show the efficiency of this new approach.