中文摘要：

发展了矩形区域上的四阶混合边值问题的广义Jacobi—Petrov-Galerkin谱方法，利用广义Jacobi多项式对模型问题的精确解进行数值展开，设计了有效的数值算法．数值结果验证了该算法的有效性和高精度．

英文摘要：

A generalized Jacobi-Petrov-Galerkin spectral method for fourth-order mixed boundary value problems in rectangular domain was developed. The numerical solution was expanded by generalized Jacobi polynomials. Efficient numerical algorithm was designed. Numerical results demonstrated the effi- ciency and high accuracy of the algorithm.