中文摘要：

在这篇论文，我们调查 Jacobi 假光谱为第四个顺序问题的方法。我们在 non-uniformlyweighted Sobolev 空格在 Jacobi-Gauss-type 插值上建立一些基本结果，它在微分、不可分的方程的数字照，和数字方法的分析用作重要工具。然后，我们为几个单个问题和第四份订单的多重维的问题建议 Jacobi pseudospectralschemes。Numericalresults 示威光谱这些计划的精确性，并且与理论分析与一致很好。

英文摘要：

In this paper, we investigate Jacobi pseudospectral method for fourth order problems. We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as important tools in analysis of numerical quadratures, and numerical methods of differential and integral equations. Then we propose Jacobi pseudospectral schemes for several singular problems and multiple-dimensional problems of fourth order. Numerical results demonstrate the spectral accuracy of these schemes, and coincide well with theoretical analysis.