共查询到20条相似文献,搜索用时 93 毫秒
1.
Michael D. Marcozzi 《Journal of Computational and Applied Mathematics》2011,235(12):3632-3645
We consider the approximation of the optimal stopping problem associated with ultradiffusion processes in the context of mathematical finance and the valuation of Asian options. In particular, the value function is characterized as the solution of an ultraparabolic variational inequality. Employing the penalty method and a regularization of the state space, we develop higher-order adaptive approximation schemes which utilize the extrapolation discontinuous Galerkin method in temporal space. Numerical examples are provided in order to demonstrate the approach. 相似文献
2.
We develop a semi-discrete approximation framework for linear nonautonomous nonhomogeneous functional differential equations of retarded type. The approximation schemes are constructed and convergence results are obtained through the approximation of an associated abstract evolution operator. Computer implementation of the schemes is outlined and a spline-based method included in the framework is constructed. Extensions of the semi-discrete methods to schemes incorporating full discretization and difference equation approximation are also discussed. Numerical results for several examples demonstrating the feasibility of the schemes are presented. 相似文献
3.
T. N. Phillips A. J. Williams 《Numerical Methods for Partial Differential Equations》2001,17(4):403-425
Semi‐Lagrangian finite volume schemes for the numerical approximation of linear advection equations are presented. These schemes are constructed so that the conservation properties are preserved by the numerical approximation. This is achieved using an interpolation procedure based on area‐weighting. Numerical results are presented illustrating some of the features of these schemes. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:403–425, 2001 相似文献
4.
《Stochastic Processes and their Applications》2020,130(8):4968-5005
This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the nonlinear part is stronger than the linear part, usually called stochastic dominated transport equations. Most standard numerical schemes lose their good stability properties on such equations, including the current linear implicit Euler method. We discretize the SPDE in space by the finite element method and propose a novel scheme called stochastic Rosenbrock-type scheme for temporal discretization. Our scheme is based on the local linearization of the semi-discrete problem obtained after space discretization and is more appropriate for such equations. We provide a strong convergence of the new fully discrete scheme toward the exact solution for multiplicative and additive noise and obtain optimal rates of convergence. Numerical experiments to sustain our theoretical results are provided. 相似文献
5.
美式期权定价问题的数值方法 总被引:21,自引:0,他引:21
本文研究美式股票看跌期权定价问题的数值方法。通过将问题转化为等价的变分不等式方程,分别建立了半离散和全离散有限元逼近格式。并给出了有限元解的收敛性和稳定性分析。数值实验表明本文算法是一个高效和收敛的算法。 相似文献
6.
Lei Yuan 《计算数学(英文版)》2009,(4):525-542
In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with an integral constraint for the state. We derive the equivalent a posteriori error estimator for the finite element approximation, which particularly suits adaptive multi-meshes to capture different singularities of the control and the state. Numerical examples are presented to demonstrate the efficiency of a posteriori error estimator and to confirm the theoretical results. 相似文献
7.
Numerical quadrature schemes of a non-conforming finite element method for general second order elliptic problems in two dimensional (2-D) and three dimensional (3-D) space are discussed in this paper. We present and analyze some optimal numerical quadrature schemes. One of the schemes contains only three sampling points, which greatly improves the efficiency of numerical computations. The optimal error estimates are derived by using some traditional approaches and techniques. Lastly, some numerical results are provided to verify our theoretical analysis. 相似文献
8.
Mauro Gaggero Giorgio Gnecco Marcello Sanguineti 《Journal of Optimization Theory and Applications》2013,156(2):380-416
Value-function approximation is investigated for the solution via Dynamic Programming (DP) of continuous-state sequential N-stage decision problems, in which the reward to be maximized has an additive structure over a finite number of stages. Conditions that guarantee smoothness properties of the value function at each stage are derived. These properties are exploited to approximate such functions by means of certain nonlinear approximation schemes, which include splines of suitable order and Gaussian radial-basis networks with variable centers and widths. The accuracies of suboptimal solutions obtained by combining DP with these approximation tools are estimated. The results provide insights into the successful performances appeared in the literature about the use of value-function approximators in DP. The theoretical analysis is applied to a problem of optimal consumption, with simulation results illustrating the use of the proposed solution methodology. Numerical comparisons with classical linear approximators are presented. 相似文献
9.
Multiphysical simulation tasks are often numerically solved by dynamic iteration schemes. Usually, this demands the efficient and stable coupling of existing simulation software for the contributing physical subdomains or subsystem. Since the coupling is weakened by such a simulation strategy, iteration is needed to enhance the quality of the numerical approximation. By the means of error recursions, one obtains estimates for the approximation order and the reduction of error per iteration (convergence rate). It is know that the first iterations can be coarsely sampled (in time), but the last iterations need to be refined (h-refinement) to obtain the accuracy gain of latter iterations (‘sweeps’). In this work we discuss an optimal choice of the approximation order p used in the time integration with respect to the iteration ‘sweep’ count. It is deduced from the analytical error recursion and yields a p-refinement strategy. Numerical experiments show that our estimates are sharp and give a precise prediction of the correct convergence. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
Yoshihiro Saito Taketomo Mitsui 《Annals of the Institute of Statistical Mathematics》1993,45(3):419-432
A lot of discrete approximation schemes for stochastic differential equations with regard to mean-square sense were proposed. Numerical experiments for these schemes can be seen in some papers, but the efficiency of scheme with respect to its order has not been revealed. We will propose another type of error analysis. Also we will show results of simulation studies carried out for these schemes under our notion. 相似文献
11.
Dong Liang Guanying SunWenqia Wang 《Journal of Computational and Applied Mathematics》2011,235(13):3841-3858
In this paper, we analyze two new second-order characteristic schemes in time and age for an age-structured population model with nonlinear diffusion and reaction. By using the characteristic difference to approximate the transport term and the average along the characteristics to treat the nonlinear spatial diffusion and reaction terms, an implicit second-order characteristic scheme is proposed. To compute the nonlinear approximation system, an explicit second-order characteristic scheme in time and age is further proposed by using the extrapolation technique. The global existence and uniqueness of the solution of the nonlinear approximation scheme are established by using the theory of variation methods, Schauder’s fixed point theorem, and the technique of prior estimates. The optimal error estimates of second order in time and age are strictly proved for both the implicit and the explicit characteristic schemes. Numerical examples are given to illustrate the performance of the methods. 相似文献
12.
Asymptotic preserving time‐discretization of optimal control problems for the Goldstein–Taylor model
Giacomo Albi Michael Herty Christian Jörres Lorenzo Pareschi 《Numerical Methods for Partial Differential Equations》2014,30(6):1770-1784
We consider the development of implicit‐explicit time integration schemes for optimal control problems governed by the Goldstein–Taylor model. In the diffusive scaling, this model is a hyperbolic approximation to the heat equation. We investigate the relation of time integration schemes and the formal Chapman–Enskog‐type limiting procedure. For the class of stiffly accurate implicit–explicit Runge–Kutta methods, the discrete optimality system also provides a stable numerical method for optimal control problems governed by the heat equation. Numerical examples illustrate the expected behavior. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1770–1784, 2014 相似文献
13.
We propose two-grid iteration methods for Symm's integral equation discretized by quadrature-collocation or quadrature methods. Asymptotically the optimal order of error estimate is achieved already on the first iteration, for some modifications on the second iteration. This enables us to introduce some solvers which are of the optimal convergence order and cheap in a practical implementation; the cost varies between O(N2) and O(N log N) arithmetic operations. Numerical experiments confirm the approximation properties of the schemes. 相似文献
14.
This paper is concerned with discrete-time hybrid filtering of linear non-Gaussian systems coupled by a hidden switching process. An optimal control approach is used to derive a finite-dimensional recursive filter which is optimal in the sense of the most probable trajectory estimate. Models with unknown switching distributions are considered. Extensions to nonlinear hybrid systems are given. Numerical examples are considered and computational experiments are reported. These examples demonstrate that our filtering scheme outperforms popular filtering schemes available in the literature. 相似文献
15.
16.
Finite difference method is an important methodology in the approximation of waves.
In this paper, we will study two implicit finite difference schemes
for the simulation of waves. They are the weighted
alternating direction implicit (ADI) scheme and the
locally one-dimensional (LOD) scheme. The approximation errors,
stability conditions, and dispersion relations for both schemes
are investigated. Our analysis shows that the LOD implicit scheme
has less dispersion error than that of the ADI scheme. Moreover, the
unconditional stability for both schemes with arbitrary spatial accuracy
is established for the first time. In order to improve
computational efficiency, numerical algorithms based on message
passing interface (MPI) are implemented. Numerical examples of wave propagation
in a three-layer model and a standard complex model are presented.
Our analysis and comparisons show that both ADI and LOD schemes
are able to efficiently and accurately simulate wave propagation
in complex media. 相似文献
17.
该文讨论了线性流形上矩阵方程AX=B反对称正交对称反问题的最小二乘解及其最佳逼近问题. 给出了最小二乘问题解集合的表达式, 得到了给定矩阵的最佳逼近问题的解, 最后给出计算任意矩阵的最佳逼近解的数值方法及算例. 相似文献
18.
该文讨论了线性流形上矩阵方程AX=B反对称正交对称反问题的最小二乘解及其最佳逼近问题.给出了最小二乘问题解集合的表达式,得到了给定矩阵的最佳逼近问题的解,最后给出计算任意矩阵的最佳逼近解的数值方法及算例. 相似文献
19.
线性流形上中心对称矩阵的最佳逼近 总被引:10,自引:1,他引:9
1 引 言令Rn×m表示所有n×m阶实矩阵集合;ORn×n表示所有n×n阶正交矩阵之集;A+表示矩阵A的Moore-Penrose广义逆;Iκ表示κ阶单位阵;||·||表示矩阵的Frobenius范数;rank(A)表示矩阵A的秩.设ei为n阶单位矩阵In的第i列(i=1,2,…,n),记Sn=(en,en-1,…,e1),易知 相似文献
20.
本文讨论了线性流形上用双反对称矩阵构造给定矩阵的最佳逼近问题,给出问题解的表达式,最后给出求最佳逼近解的数值方法与数值算例. 相似文献