In this paper, we propose a new weak second-order numerical scheme for solving stochastic differential equations with jumps. By using trapezoidal rule and the integration-by-parts formula of Malliavin calculus, we theoretically prove that the numerical scheme has second-order convergence rate. To demonstrate the effectiveness and the second-order convergence rate, three numerical experiments are given.

In this paper, we propose a new weak order 2.0 numerical scheme for solving stochastic differential equations with Markovian switching (SDEwMS). Using the Malliavin stochastic analysis, we theoretically prove that the new scheme has local weak order 3.0 convergence rate. Combining the special property of Markov chain, we study the effects from the changes of state space on the convergence rate of the new scheme. Two numerical experiments are given to verify the theoretical results.

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For the problems of complex structure, unclear network and fuzzy boundary of power distribution network, grid planning is carried out in the power distribution network according to the idea of “Divide it into small grids, and manage separately”. Firstly, according to the modularization idea and the rule of land use and time development, a three-level grid planning system of power supply functional area, power supply mesh and power supply unit is constructed. Secondly, in the grid planning system, the spatial load forecasting method is given at three levels from bottom to top: at the level of power supply unit, the recommended value of saturated load density index is given, and the calculation method of the simultaneity rate in power supply unit is put forward. At the level of power supply mesh, based on the land nature of each power supply unit, the simultaneity rate of different land is given. Finally, based on the actual planning case of a certain region, the effectiveness of the grid planning method is verified.