A survey of numerical methods for stochastic differential equations     

P. E. Kloeden  E. Platen 《Stochastic Environmental Research and Risk Assessment (SERRA)》1989,3(3):155-178

The development of numerical methods for stochastic differential equations has intensified over the past decade. The earliest methods were usually heuristic adaptations of deterministic methods, but were found to have limited accuracy regardless of the order of the original scheme. A stochastic counterpart of the Taylor formula now provides a framework for the systematic investigation of numerical methods for stochastic differential equations. It suggests numerical schemes, which involve multiple stochastic integrals, of higher order of convergence. We shall survey the literature on these and on the earlier schemes in this paper. Our discussion will focus on diffusion processes, but we shall also indicate the extensions needed to handle processes with jump components. In particular, we shall classify the schemes according to strong or weak convergence criteria, depending on whether the approximation of the sample paths or of the probability distribution is of main interest.  相似文献   

Stochastic analysis of estuarine hydraulics     

R. Willis  B. A. Finney  M. McKee  A. Militello 《Stochastic Environmental Research and Risk Assessment (SERRA)》1989,3(2):71-84

A new methodology is presented for the solution of the stochastic hydraulic equations characterizing steady, one-dimensional estuarine flow. The methodology is predicated on quasi-linearization, perturbation methods, and the finite difference approximation of the stochastic differential operators. Assuming Manning's roughness coefficient is the principal source of uncertainty in the model, stochastic equations are presented for the water depths and flow rates in the estuarine system. Moment equations are developed for the mean and variance of the water depths. The moment equations are compared with the results of Monte Carlo simulation experiments. The results confirm that for any spatial location in the estuary that (1) as the uncertainty in the channel roughness increases, the uncertainty in mean depth increases, and (2) the predicted mean depth will decrease with increasing uncertainty in Manning'sn. The quasi-analytical approach requires significantly less computer time than Monte Carlo simulations and provides explicit  相似文献   

Analytical techniques for the estimation of mine water inflow   总被引：1，自引：0，他引：1  

Singh  R. N.  Atkins  A. S. 《Geotechnical and Geological Engineering》1985,3(1):65-77

Summary This paper outlines various analytical techniques for mine water inflow estimation incorporating several refinements such as finite boundary conditions, linear, fracture and turbulent flow conditions to pumping wells and underground excavations. These modifications enable practical mining to be simulated and therefore, permit more accurate predictions of mine inflow quantities. Application of these techniques are given together with the scope of the application.  相似文献   

Semigroup solutions to stochastic unsteady groundwater flow subject to random parameters     

S. E. Serrano  T. E. Unny 《Stochastic Environmental Research and Risk Assessment (SERRA)》1987,1(4):281-296

Two methods for the solution of partial differential equations (PDE) for the general case of random in time physical parameters are presented and their application to the solution of unsteady regional groundwater flow equations are illustrated. The first method is the semigroup approach which directly offers a solution without resorting to closure approximations (hierarchy techniques), perturbation techniques, or Montecarlo simulation techniques. The semigroup approach can also handle the general stochastic problem when randomness also appears as initial conditions, boundary conditions or forcing terms. The second method is an approximation scheme to obtain the semigroup solution in complex cases and permits the solution of equations with more than one random coefficient.  相似文献   

Least squares parameter estimation in chaotic differential equations     

Josef Kallrath  Johannes P. Schlöder  Hans Georg Bock 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):353-371

A recent least squares algorithm, which is designed to adapt implicit models to given sets of data, especially models given by differential equations or dynamical systems, is reviewed and used to fit the Hénon-Heiles differential equations to chaotic data sets.This numerical approach for estimating parameters in differential equation models, called theboundary value problem approach, is based on discretizing the differential equations like a boundary value problem,e.g. by a multiple shooting or collocation method, and solving the resulting constrained least squares problem with a structure exploiting generalized Gauss-Newton-Method (Bock, 1981).Dynamical systems like the Hénon-Heiles system which can have initial values and parameters that lead to positive Lyapunov exponents or phase space filling Poincaré maps give rise to chaotic time series. Various scenarios representing ideal and noisy data generated from the Hénon-Heiles system in the chaotic region are analyzedw.r.t. initial conditions, parameters and Lyapunov exponents. The original initial conditions and parameters are recovered with a given accuracy. The Lyapunov spectrum is then computed directly from the identified differential equations and compared to the spectrum of the true dynamics.presently at IWR, Universität Heidelberg, Im Neuenheimer Feld 368, D-6900 Heidelberg, Germany  相似文献   

THM Coupled Modeling in Near Field of an Assumed HLW Deep Geological Disposal Repository     

ShenZhenyao LiGuoding LiShushen 《中国地质大学学报(英文版)》2004,15(4):388-394

One of the most suitable ways under study for the disposal of high-level radioactive waste (HLW) is isolation in deep geological repositories. It is very important to research the thermo-hydromechanical (THM) coupled processes associated with an HLW disposal repository. Non-linear coupled equations, which are used to describe the THM coupled process and are suited to saturated-unsaturated porous media, are presented in this paper. A numerical method to solve these equations is put forward, and a finite element code is developed. This code is suited to the plane strain or axis-symmetry problem. Then this code is used to simulate the THM coupled process in the near field of an ideal disposal repository. The temperature vs. time, hydraulic head vs. time and stress vs. time results show that, in this assumed condition, the impact of temperature is very long (over 10 000 a) and the impact of the water head is short (about 90 d). Since the stress is induced by temperature and hydraulic head in this condition, the impact time of stress is the same as that of temperature. The results show that THM coupled processes are very important in the safety analysis of an HLW deep geological disposal repository.  相似文献   

An Archean(?) to Paleozoic Evolution for a Garnet Peridotite Lens with Sub-Baltic Shield Affinity within the Seve Nappe Complex of Jamtland, Sweden, Central Scandinavian Caledonides   总被引：2，自引：0，他引：2  

BRUECKNER  HANNES K.; VAN ROERMUND  HERMAN L. M.; PEARSON  NORMAN J. 《Journal of Petrology》2004,45(2):415-437

Mineralogical, isotopic, geochemical and geochronological evidencedemonstrates that the Friningen body, a garnet peridotite bodycontaining garnet pyroxenite layers in the Seve Nappe Complex(SNC) of Northern Jämtland, Sweden, represents old, certainlyProterozoic and possibly Archean, lithosphere that became incorporatedinto the Caledonian tectonic edifice during crustal subductioninto the mantle at c. 450 Ma. Both garnet peridotite and pyroxenitecontain two (M₁ and M₂) generations of garnet-bearing assemblagesseparated by the formation of two-pyroxene, spinel symplectitearound the M₁ garnet and the crystallization of low-Cr spinel_1Cin the matrix. These textures suggest initial high-pressure(HP) crystallization of garnet peridotite and pyroxenite succeededby decompression into the spinel stability field, followed byrecompression into the garnet peridotite facies. Some pyroxenitelayers appear to be characterized solely by M₂ assemblages withstretched garnet as large as several centimeters. Laser ablationmicroprobe–inductively coupled plasma mass spectrometryRe–Os analyses of single sulfide grains generally definemeaningless model ages suggesting more than one episode of Reand/or Os addition and/or loss to the body. Pentlandite grainsfrom a single polished slab of one garnet peridotite, however,define a linear array on an Re–Os isochron diagram that,if interpreted as an errorchron, suggests an Archean melt extractionevent that left behind the depleted dunite and harzburgite bodiesthat characterize the SNC. Refertilization of this mantle bymelts associated with the development of the pyroxenite layersis indicated by enriched clinopyroxene Sr–Nd isotope ratios,and by parallel large ion lithophile-enriched trace elementpatterns in clinopyroxene from pyroxenite and the immediatelyadjacent peridotite. Clinopyroxene and whole-rock model Sm–Ndages (T_DM = 1·1–2·2 Ga) indicate that fertilizationtook place in Proterozoic times. Sm–Nd garnet₂–clinopyroxene₂–wholerock ± orthopyroxene₂ mineral isochrons from three pyroxenitelayers define overlapping ages of 452·1 ± 7·5and 448 ± 13 Ma and 451 ± 43 Ma (2  相似文献   

Deep and High-temperature Hydrothermal Circulation in the Oman Ophiolite--Petrological and Isotopic Evidence   总被引：2，自引：0，他引：2  

BOSCH  D.; JAMAIS  M.; BOUDIER  F.; NICOLAS  A.; DAUTRIA  J.-M.; AGRINIER  P. 《Journal of Petrology》2004,45(6):1181-1208

A systematic search for evidence of high-temperature hydrousalteration within the gabbros of the Samail ophiolite (Oman)shows that most of the gabbros have been affected by successivestages of alteration, starting above 975°C and ending below500°C. Sr and O isotopic analyses provide constraints onthe nature and origin of the fluids associated with these alterationevents. Massive gabbros, dykes and veins and their associatedminerals depart from mid-ocean ridge basalt (MORB)-source magmasignatures (⁸⁷Sr/⁸⁶Sr >0·7032 and depleted  相似文献   

异轨遥感立体像对外方位元素的求解算法   总被引：4，自引：1，他引：4  

张永军  张剑清 《武汉大学学报(信息科学版)》2003,28(5):521-524

在对异轨遥感立体像对外方位元素求解的基本模型进行系统阐述的基础上 ,讨论了基于共面条件的后方交会模型改化方法及其和基于共线方程的后方交会模型的融合。给出了外方位元素初值求解的实用算法 ,并利用实测立体像对数据进行了联合平差计算 ,取得了较好的结果  相似文献   

晚新生代天山隆升与库车坳陷构造转换的沉积约束   总被引：31，自引：2，他引：31  

李忠  王清晨  王道轩  林伟 《沉积学报》2003,21(1):38-45

对库车坳陷库车河剖面不同尺度沉积碎屑组分的系统分析发现 ,晚第三纪以来类磨拉石及其中不稳定碎屑矿物组合开始发育 ,并在中新世后发生显著增加。沉积体系研究表明 ,库车坳陷自白垩纪以来粗粒冲积体系前锋、沉积中心逐步向南迁移 ;但该规律自上新世开始发生了明显转变 ,表现为上新世库车组、上 -更新世西域组冲积体系整体大尺度南移 ,而沉积中心则相对北移 ,盆地北部沉积边界与现存盆山边界大致可以对比 ,并受到南倾同沉积正断裂的控制。对比天山区域构造、古气候演变资料 ,认为上述沉积记录是晚新生代强烈挤压应力作用下天山构造隆升加剧 ,并在上新世以后由于重力作用诱发库车坳陷 -天山浅部构造层伸展、坍塌的结果。对这一构造转换的认识修订了库车坳陷新生代构造调整的序列。  相似文献