中文摘要：

用奇异值分解和特征投影分解（proper orthogonal decomposition,简记POD）方法建立Sobolev方程的一种降阶外推有限差分算法,并给出误差估计.最后用数值例子,验证基于POD方法降阶外推有限差分算法的可行性和有效性.

英文摘要：

The singular value decomposition technique and the proper orthogonal decomposition（POD）method were applied to establish a reduced-order extrapolating finite difference algorithm for Sobolev equations.Firstly,the absolutely stable fully 2nd-order accurate Crank-Nicolson（C-N） scheme for Sobolev equations was built,and the C-N reduced-order extrapolating finite difference algorithm was constructed based onthe POD method,where the number of unknowns in numerical computation was greatly reduced.Secondly,the error estimates of the reduced-order finite difference solutions were provided.Finally,a numerical example was used to verify the feasibility and efficiency of the proposed reduced-order extrapolating finite difference algorithm.