We focus on developing the finite difference (i.e., backward Euler difference or second-order central difference)/local discontinuous Galerkin finite element mixed method to construct and analyze a kind of efficient, accurate, flexible, numerical schemes for approximately solving time-space fractional subdiffusion/superdiffusion equations. Discretizing the time Caputo fractional derivative by using the backward Euler difference for the derivative parameter (0<α<1) or second-order central difference method for (1<α<2), combined with local discontinuous Galerkin method to approximate the spatial derivative which is defined by a fractional Laplacian operator, two high-accuracy fully discrete local discontinuous Galerkin (LDG) schemes of the time-space fractional subdiffusion/superdiffusion equations are proposed, respectively. Through the mathematical induction method, we show the concrete analysis for the stability and the convergence under theL2norm of the LDG schemes. Several numerical experiments are presented to validate the proposed model and demonstrate the convergence rate of numerical schemes. The numerical experiment results show that the fully discrete local discontinuous Galerkin (LDG) methods are efficient and powerful for solving fractional partial differential equations.
From the level of agricultural material equipment, the level of agricultural output benefit, the level of agricultural economic structure, the level of agricultural industrialization management, the level of agricultural sustainable development, and the level of rural social and economic development, based on 15 indicators, an index system for evaluating the comprehensive capacity of modern agricultural development in Huizhou was constructed. The comprehensive evaluation of the development level of modern agriculture in Huizhou from 2012 to 2018 was measured by the entropy weight method, and the evaluation was analyzed with the average level of Guangdong Province. We find out the gap between the development advantages of Huizhou and the average level of Guangdong Province, so as to promote the development of modern agriculture in Huizhou. Based on the comprehensive evaluation index of the development level of modern agriculture in Huizhou from 2012 to 2018 obtained by the entropy weight method, a fractional cumulative grey GM (1, 1) forecasting model was established, and its development ability was predicted and analyzed. The forecast result has certain guiding significance to the development of modern agriculture in Huizhou.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.