Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalised weighted residual method (GWRM), is a generalisatio...Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalised weighted residual method (GWRM), is a generalisation of weighted residual methods to the time and parameter domains [1]. A semi-analytical Chebyshev polynomial ansatz is employed, and the problem reduces to determine the coefficients of the ansatz from linear or nonlinear algebraic systems of equations. In order to avoid large memory storage and computational cost, it is preferable to subdivide the temporal and spatial domains into subdomains. Methods and examples of this article demonstrate how this can be achieved.展开更多
采用小波分析、低通滤波、相关分析、逐步回归以及最优子集回归等方法建立斗门开汛日期的预测模型。将开汛日期序列分解为年际变化和年代际变化2个分量,分别研究其与前期冬季500h Pa高度场、850 h Pa风场、海平面气压场和海温场的相关性...采用小波分析、低通滤波、相关分析、逐步回归以及最优子集回归等方法建立斗门开汛日期的预测模型。将开汛日期序列分解为年际变化和年代际变化2个分量,分别研究其与前期冬季500h Pa高度场、850 h Pa风场、海平面气压场和海温场的相关性,并将显著相关区域作为初选因子。通过逐步回归将因子数限制在10个以内,最后应用最优子集回归建立预测模型。结果表明:这种分离时间尺度的回归预测模型具有较好的拟合效果,计算得出的回归序列与原距平序列相关系数为0.81,两者同号率为77.8%,其中相差±7 d以内年份约占42.2%;相差±15 d以内的年份约占75.6%。最后对2012—2014年开汛日期进行试报,其中2012和2014年试报效果较好,误差分别为-5.89和-10.45 d。展开更多
文摘Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalised weighted residual method (GWRM), is a generalisation of weighted residual methods to the time and parameter domains [1]. A semi-analytical Chebyshev polynomial ansatz is employed, and the problem reduces to determine the coefficients of the ansatz from linear or nonlinear algebraic systems of equations. In order to avoid large memory storage and computational cost, it is preferable to subdivide the temporal and spatial domains into subdomains. Methods and examples of this article demonstrate how this can be achieved.
