In this paper,a kind of explicit difference scheme to solve nonlinear evolution equations,perfectly keeping the square conservation by adjusting the time step interval,is constructed,from the comprehensive maintenance...In this paper,a kind of explicit difference scheme to solve nonlinear evolution equations,perfectly keeping the square conservation by adjusting the time step interval,is constructed,from the comprehensive maintenance of the ad- vantages of the implicit complete square conservative scheme and the explicit instantaneous square conservative scheme. The new schemes are based on the thought of adding a small dissipation,but it is different from the small dissipation method.The dissipative term used in the new schemes is not a simple artificial dissipative term,but a so-called (time) harmonious dissipative term that can compensate for the truncation errors from the dissociation of the time differential term.Therefore,the new schemes may have a high time precision and may acquire a satisfactory effect in numerical tests.展开更多
This paper describes the procedure of using the GM (1,1) weighted Markov chain (GMWMC) to forecast the utility water supply, a quantity that usually has significant temporal variability. The GMWMC is formulated into f...This paper describes the procedure of using the GM (1,1) weighted Markov chain (GMWMC) to forecast the utility water supply, a quantity that usually has significant temporal variability. The GMWMC is formulated into five steps: (1) use GM (1,1) to fit the trend of the data, and obtain the relative error of the fitted values; (2) divide the relative error into ‘state’ data based on pre-set intervals; (3) calibrate the weighted Markov chain model: herein the parameters are the pre-set interval and the step of transition matrix (TM); (4) by using auto-correlation coefficient as the weight, the Markov chain provides the prediction interval. Then the mid-value of the interval is selected as the relative error for the data. Upon combining the data and its relative error, the predicted magnitude in a specific time period is obtained; and, (5) validate the model. Commonly, static intervals are used in both model calibration and validation stages, usually causing large errors. Thus, a dynamic adjustment interval (DAI) is proposed for a better performance. The proposed procedure is described and demonstrated through a case study, which shows that the DAI can usually achieve a better performance than the static interval, and the best TM may exist for certain data.展开更多
文摘In this paper,a kind of explicit difference scheme to solve nonlinear evolution equations,perfectly keeping the square conservation by adjusting the time step interval,is constructed,from the comprehensive maintenance of the ad- vantages of the implicit complete square conservative scheme and the explicit instantaneous square conservative scheme. The new schemes are based on the thought of adding a small dissipation,but it is different from the small dissipation method.The dissipative term used in the new schemes is not a simple artificial dissipative term,but a so-called (time) harmonious dissipative term that can compensate for the truncation errors from the dissociation of the time differential term.Therefore,the new schemes may have a high time precision and may acquire a satisfactory effect in numerical tests.
基金Project supported by the National Natural Science Foundation of China (No. 50778121)the National Basic Research Program of China (No. 2007CB407306-1)the National Water Pollution Control and Management of Science and Technology Project of China (No. 2008ZX07317-005)
文摘This paper describes the procedure of using the GM (1,1) weighted Markov chain (GMWMC) to forecast the utility water supply, a quantity that usually has significant temporal variability. The GMWMC is formulated into five steps: (1) use GM (1,1) to fit the trend of the data, and obtain the relative error of the fitted values; (2) divide the relative error into ‘state’ data based on pre-set intervals; (3) calibrate the weighted Markov chain model: herein the parameters are the pre-set interval and the step of transition matrix (TM); (4) by using auto-correlation coefficient as the weight, the Markov chain provides the prediction interval. Then the mid-value of the interval is selected as the relative error for the data. Upon combining the data and its relative error, the predicted magnitude in a specific time period is obtained; and, (5) validate the model. Commonly, static intervals are used in both model calibration and validation stages, usually causing large errors. Thus, a dynamic adjustment interval (DAI) is proposed for a better performance. The proposed procedure is described and demonstrated through a case study, which shows that the DAI can usually achieve a better performance than the static interval, and the best TM may exist for certain data.
