Numerical Solution Of Stochastic Differential Equations With Application To Flood Regulating Calculation Of Reservoir

par In the actual engineering,with improving of model accuracy and practical problem complexity,more and more uncertain factors are considered in the model establishment.By introducing random factors on differential equation ,stochastic differential equation is formed.With the development of science and technology,stochastic differential equations are more and more used in engineering.In my thesis,After analyzing the Brownian motion characteristics of reservoir capacity in flood regulation,mathematics methods and strategies are used to analyze the problem in flood regulation,the author proposes an It(?) stochastic differential equation including random term to describe and analyze the stochastic rules of reservoir level hydrography in flood routing process.An expression of active risk for the flood relief is given,and the probability densities of reservoir level hydrography,which is related to the risk for the flood relief are computed by Euler method.If also calculates the mean value at different time of the process of water level as well probability of overflowing ,with corresponding formula.Furthermore,it compares the water level under stochastic distribution with the different strengths in order to ascertain more the stochastic differential equations is fixable.Bused on process of the water level of a reservoir satisfying stochastic differential equations during process of releasing floodwater,this paper simulates the water level and its fluctuation under stochastic disturbance of Brownian motion by means of numerical solution of stochastic differential equations.Analyzed and calculated results indicate that by using the stochastic differential equations in flood routing,the influence of various random factors on the reservoir level hydrography Can be comprehensively analyzed.Therefore,the method of risk analysis suggested by this paper is reasonable.It is helpful for the flood practice.The main work of my thesis is as following:1.introduced basic knowledge.Involves the concept of random process. commonly used in several hydrological random process,the concept of stochastic differential equations,It(?) stochastic differential equations,solution of stochastic differential equations of Euler's method and its stability,and several commonly used hydrologic concepts.2,The physical background is studied,and the mathematics essence is drawn.The corresponding It(?) stochastic differential equations are given by introducing the random factors that really exist on original physical model,and its characteristic is studied.3,Advanced flood Regulating Calculation of Reservoir and flood risk analysis. Application of hydrology,hydraulics formula,and the solution of It(?) stochastic differential equation of the Euler approximation method to calculate the probability of flood dam diffuse.4,Random numerical simulation.Using the above theory and formula to simulate the reservoir water level line,at different intensities of the flood hydrography to calculate the probability of various overflowing.