Download or read book Numerical Solution of Dynamic Equilibrium Models Under Poisson Uncertainty written by Olaf Posch and published by . This book was released on 2011 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Computations Theory and Algorithms written by Yaroslav D. Sergeyev and published by Springer Nature. This book was released on 2020-02-13 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 11973 and 11974 constitute revised selected papers from the Third International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2019, held in Crotone, Italy, in June 2019. This volume, LNCS 11974, consists of 19 full and 32 short papers chosen among regular papers presented at the the Conference including also the paper of the winner (Lorenzo Fiaschi, Pisa, Italy) of The Springer Young Researcher Prize for the best NUMTA 2019 presentation made by a young scientist. The papers in part II explore the advanced research developments in such interconnected fields as local and global optimization, machine learning, approximation, and differential equations. A special focus is given to advanced ideas related to methods and applications using emerging computational paradigms.

Download or read book Numerical Solution of Dynamic Equilibrium Equations written by Jamal J. Nasir and published by . This book was released on 1983 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Calculating and Using Second Order Accurate Solutions of Discrete Time Dynamic Equilibrium Models written by and published by . This book was released on 2003 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Uncertainty Quantification and Sensitivity Analysis for Multiscale Kinetic Equations with Random Inputs written by Ruiwen Shu and published by . This book was released on 2018 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis gives an overview of the current results on uncertainty quantification and sensitivity analysis for multiscale kinetic equations with random inputs, with an emphasis on the author's contribution to this field. In the first part of this thesis we consider a kinetic-fluid model for disperse two-phase flows with uncertainty in the fine particle regime. We propose a stochastic asymptotic-preserving (s-AP) scheme in the generalized polynomial chaos stochastic Galerkin (gPC-sG) framework, which allows the efficient computation of the problem in both kinetic and hydrodynamic regimes. The s-AP property is proved by deriving the equilibrium of the gPC version of the Fokker-Planck operator. The coefficient matrices that arise in a Helmholtz equation and a Poisson equation, essential ingredients of the algorithms, are proved to be positive definite under reasonable and mild assumptions. The computation of the gPC version of a translation operator that arises in the inversion of the Fokker-Planck operator is accelerated by a spectrally accurate splitting method. Numerical examples illustrate the s-AP property and the efficiency of the gPC-sG method in various asymptotic regimes. In the second part of this thesis we consider the same kinetic-fluid model with random initial inputs in the light particle regime. Using energy estimates, we prove the uniform regularity in the random space of the model for random initial data near the global equilibrium in some suitable Sobolev spaces, with the randomness in the initial particle distribution and fluid velocity. By hypocoercivity arguments, we prove that the energy decays exponentially in time, which means that the long time behavior of the solution is insensitive to such randomness in the initial data. Then we consider the gPC-sG method for the same model. For initial data near the global equilibrium and smooth enough in the physical and random spaces, we prove that the gPC-sG method has spectral accuracy, uniformly in time and the Knudsen number, and the error decays exponentially in time. In the third part of this thesis we propose a stochastic Galerkin method using sparse wavelet bases for the Boltzmann equation with multi-dimensional random inputs. The method uses locally supported piecewise polynomials as an orthonormal basis of the random space. By a sparse approach, only a moderate number of basis functions is required to achieve good accuracy in multi-dimensional random spaces. We discover a sparse structure of a set of basis-related coefficients, which allows us to accelerate the computation of the collision operator. Regularity of the solution of the Boltzmann equation in the random space and an accuracy result of the stochastic Galerkin method are proved in multi-dimensional cases. The efficiency of the method is illustrated by numerical examples with uncertainties from the initial data, boundary data and collision kernel. In the fourth part of this thesis we explore the possibility of using Generalized polynomial chaos (gPC) for uncertainty quantification in hyperbolic problems. GPC has been extensively used in uncertainty quantification problems to handle random variables. For gPC to be valid, one requires high regularity on the random space that hyperbolic type problems usually cannot provide, and thus it is believed to behave poorly in those systems. We provide a counter-argument, and show that despite the solution profile itself develops singularities in the random space, which prevents the use of gPC, the physical quantities such as shock emergence time, shock location, and shock width are all smooth functions of random variables in the initial data: with proper shifting, the solution's polynomial interpolation approximates with high accuracy. The studies were inspired by the stability results from hyperbolic systems. We use the Burgers' equation as an example for thorough analysis, and the analysis could be extended to general conservation laws with convex fluxes.

Download or read book Numerical Methods in Geotechnical Engineering IX written by António S. Cardoso and published by CRC Press. This book was released on 2018-06-19 with total page 2430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods in Geotechnical Engineering IX contains 204 technical and scientific papers presented at the 9th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE2018, Porto, Portugal, 25—27 June 2018). The papers cover a wide range of topics in the field of computational geotechnics, providing an overview of recent developments on scientific achievements, innovations and engineering applications related to or employing numerical methods. They deal with subjects from emerging research to engineering practice, and are grouped under the following themes: Constitutive modelling and numerical implementation Finite element, discrete element and other numerical methods. Coupling of diverse methods Reliability and probability analysis Large deformation – large strain analysis Artificial intelligence and neural networks Ground flow, thermal and coupled analysis Earthquake engineering, soil dynamics and soil-structure interactions Rock mechanics Application of numerical methods in the context of the Eurocodes Shallow and deep foundations Slopes and cuts Supported excavations and retaining walls Embankments and dams Tunnels and caverns (and pipelines) Ground improvement and reinforcement Offshore geotechnical engineering Propagation of vibrations Following the objectives of previous eight thematic conferences, (1986 Stuttgart, Germany; 1990 Santander, Spain; 1994 Manchester, United Kingdom; 1998 Udine, Italy; 2002 Paris, France; 2006 Graz, Austria; 2010 Trondheim, Norway; 2014 Delft, The Netherlands), Numerical Methods in Geotechnical Engineering IX updates the state-of-the-art regarding the application of numerical methods in geotechnics, both in a scientific perspective and in what concerns its application for solving practical boundary value problems. The book will be much of interest to engineers, academics and professionals involved or interested in Geotechnical Engineering.

Download or read book Mathematical Modelling and Numerical Methods in Finance written by Alain Bensoussan and published by Elsevier. This book was released on 2009-06-16 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. Coverage of all aspects of quantitative finance including models, computational methods and applications Provides an overview of new ideas and results Contributors are leaders of the field

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 956 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Solving Dynamic General Equilibrium Models Using a Second Order Approximation to the Policy Function written by Stephanie Schmitt-Grohé and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper derives a second-order approximation to the solution of a general class of discrete-time rational expectations models. The main theoretical contribution of the paper is to show that for any model belonging to the general class considered, the coefficients on the terms linear and quadratic in the state vector in a second-order expansion of the decision rule are independent of the volatility of the exogenous shocks. In other words, these coefficients must be the same in the stochastic and the deterministic versions of the model. Thus, up to second order, the presence of uncertainty affects only the constant term of the decision rules. In addition, the paper presents a set of MATLAB programs designed to compute the coefficients of the second-order approximation. The validity and applicability of the proposed method is illustrated by solving the dynamics of a number of model economies.

Download or read book Uncertainty Quantification for Multiscale Kinetic Equations and Quantum Dynamics written by Liu Liu and published by . This book was released on 2017 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first part of the thesis, we develop a generalized polynomial chaos approach based stochastic Galerkin (gPC-SG) method for the linear semi-conductor Boltzmann equation with random inputs and diffusive scalings. The random inputs are due to uncertainties in the collision kernel or initial data. We study the regularity (uniform in the Knudsen number) of the solution in the random space, and prove the spectral accuracy of the gPC-SG method. We then use the asymptotic-preserving framework for the deterministic counterpart to come up with the stochastic asymptotic-preserving (sAP) gPC-SG method for the problem under study which is efficient in the diffusive regime. Numerical experiments are conducted to validate the accuracy and asymptotic properties of the method. In the second part, we study the linear transport equation under diffusive scaling and with random inputs. The method is based on the gPC-SG framework. Several theoretical aspects will be addressed. A uniform numerical stability with respect to the Knudsen number and a uniform error estimate is given. For temporal and spatial discretizations, we apply the implicit-explicit (IMEX) scheme under the micro-macro decomposition framework and the discontinuous Galerkin (DG) method. A rigorous proof of the sAP property is given. Extensive numerical experiments that validate the accuracy and sAP of the method are shown. In the last part, we study a class of highly oscillatory transport equations that arise in semiclassical modeling of non-adiabatic quantum dynamics. These models contain uncertainties, particularly in coefficients that correspond to the potentials of the molecular system. We first focus on a highly oscillatory scalar model with random uncertainty. Our method is built upon the nonlinear geometrical optics (NGO) based method for numerical approximations of deterministic equations, which can obtain accurate pointwise solution even without numerically resolving spatially and temporally the oscillations. With the random uncertainty, we show that such a method has oscillatory higher order derivatives in the random space, thus requires a frequency dependent discretization in the random space. We modify this method by introducing a new "time" variable based on the phase, which is shown to be non-oscillatory in the random space, based on which we develop a gPC-SG method that can capture oscillations with the frequency-independent time step, mesh size as well as the degree of polynomial chaos. A similar approach is then extended to a semiclassical surface hopping model system with a similar numerical conclusion. Various numerical examples attest that these methods indeed capture accurately the solution statistics pointwisely even though none of the numerical parameters resolve the high frequencies of the solution.

Download or read book Controlled Stochastic Differential Equations Under Poisson Uncertainty and with Unbounded Utility written by Ken Sennewald and published by . This book was released on 2005 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Applied Computational Economics and Finance written by Mario J. Miranda and published by MIT Press. This book was released on 2004-08-20 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a variety of computational methods used to solve dynamic problems in economics and finance. It emphasizes practical numerical methods rather than mathematical proofs and focuses on techniques that apply directly to economic analyses. The examples are drawn from a wide range of subspecialties of economics and finance, with particular emphasis on problems in agricultural and resource economics, macroeconomics, and finance. The book also provides an extensive Web-site library of computer utilities and demonstration programs. The book is divided into two parts. The first part develops basic numerical methods, including linear and nonlinear equation methods, complementarity methods, finite-dimensional optimization, numerical integration and differentiation, and function approximation. The second part presents methods for solving dynamic stochastic models in economics and finance, including dynamic programming, rational expectations, and arbitrage pricing models in discrete and continuous time. The book uses MATLAB to illustrate the algorithms and includes a utilities toolbox to help readers develop their own computational economics applications.

Download or read book Error Estimation and Uncertainty Propagation in Computational Fluid Mechanics written by J. Z. Zhu and published by . This book was released on 2002 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Journal of Research of the National Bureau of Standards written by United States. National Bureau of Standards and published by . This book was released on 1988 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Calculating and Using Second Order Accurate Solutions of Discrete Time Dynamic Equilibrium Models written by Jinill Kim and published by . This book was released on 2003 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Equilibrium Uncertainty and Dynamics written by L. Hoogduin and published by . This book was released on 1987 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Trade Theory and Econometrics written by James R. Melvin and published by Routledge. This book was released on 2012-08-06 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together cutting edge contributions in the fields of international economics, micro theory, welfare economics and econometrics, with contributions from Donald R. Davis, Avinash K. Dixit, Tadashi Inoue, Ronald W. Jones, Dale W. Jorgenson, K. Rao Kadiyala, Murray C. Kemp, Kenneth M. Kletzer, Anne O. Krueger, Mukul Majumdar, Daniel McFadden, Lionel McKenzie, James R. Melvin, James C. Moore, Takashi Negishi, Yoshihiko Otani, Raymond Riezman, Paul A. Samuelson, Joaquim Silvestre and Marie Thursby.