A uniqueness criterion for linear problems of wave-body interaction

The question of uniqueness for linearized problems describinginteraction of submerged bodies with an ideal unbounded fluidis far from its final resolution. In this work a new criterionof uniqueness is suggested based on Green's integral identityand maximum principles for elliptic differential equations.The criterion is formulated as an inequality involving integralsof the Green function over the bodies' wetted surfaces. Thiscriterion is quite general and applicable for any number ofsubmerged bodies of arbitrary shape (provided the boundary issufficiently regular) and in any dimension; it can also be generalizedto more complicated elliptic problems. Very simple bounds arealso derived from the criterion, which deliver uniqueness setsin the space of parameters defined by submergence of the systemof bodies and the frequency of oscillation. Results of numericalinvestigation and comparison with known uniqueness criteriaare presented.     

Numerical methods for steady-state mode interactions

Mock interactions on nontrivial solutions for problems withZ₂ x Z₂ symmetry are considered. It is assumed that a path ofbifurcation points is being followed with two parameters anda mode interaction then corresponds to two separate bifurcationsof an extended system. This view of mode interactions leadsto efficient numerical methods for dealing with such pointsand for swapping onto the new paths of bifurcation points whichoriginate them. The nondegeneracy conditions associated withmode interactions are also interpreted in this context.     

雷达波形设计的一个数值方法

考虑了雷达成像中的一个波形设计问题.基于匹配滤波,在Sobolev空间的框架下,使用Hermite多项式理论,并通过一种数值算法,实现了波形的优化设计.数值实验表明,该方法是有效的.相比于CW(continuous wave)脉冲和线性调频脉冲方法,该方法可以得到更高的分辨率.     

Numerical method for solving diffusion-wave phenomena

We find solutions for the diffusion-wave problem in 1D with n-term time fractional derivatives whose orders belong to the intervals (0,1),(1,2) and (0,2) respectively, using the method of the approximation of the convolution by Laguerre polynomials in the space of tempered distributions. This method transfers the diffusion-wave problem into the corresponding infinite system of linear algebraic equations through the coefficients, which are uniquely solvable under some relations between the coefficients with index zero.The method is applicable for nonlinear problems too.     

Numerical method for an integral-algebraic system

We present a numerical method for solving the system of integral-algebraic equations arising in the study of the oblique derivative problem for the Laplace equation outside open curves on the plane. The problem describes the electric current in a semiconductor film with curvilinear electrodes in the presence of a magnetic field. The integral-algebraic system has singularities, and the kernel in the integral equation is represented in the form of a Cauchy integral. The numerical scheme is of the second approximation order despite the singularities.     

美式期权定价的数值方法

介绍了定价美式期权的几种常见数值方法.对最近几年的主要研究成果做了简单的介绍和比较,并给出了数值算例.特别回顾了美式期权定价的蒙特卡罗模拟加速方法.     

Numerical simulations for tumor and cellular immune system interactions in lung cancer treatment

We investigate a new mathematical model that describes lung cancer regression in patients treated by chemotherapy and radiotherapy. The model is composed of nonlinear integro-differential equations derived from the so-called kinetic theory for active particles and a new sink function is investigated according to clinical data from carcinoma planoepitheliale. The model equations are solved numerically and the data are utilized in order to find their unknown parameters. The results of the numerical experiments show a good correlation between the predicted and clinical data and illustrate that the mathematical model has potential to describe lung cancer regression.     

Generalization of the Bardeen-Cooper-Schrieffer method for pair interactions

We consider the transition to temperature-dependent equations for ultrasecond-quantized problems. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 3, pp. 584–592, March, 2008.     

Numerical experiments with a multistep Radau method

This paper describes an implementation of multistep collocation methods, which are applicable to stiff differential problems, singular perturbation problems, and D.A.E.s of index 1 and 2.These methods generalize one-step implicit Runge-Kutta methods as well as multistep one-stage BDF methods. We give numerical comparisons of our code with two representative codes for these methods, RADAU5 and LSODE.     

Numerical realization of the inverse scattering method

Institute of Metal Physics, Ural Scientific Center of the USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 83, No. 3, pp. 323–333, June, 1990.     

Numerical study of the incremental unknowns method

Through numerical experiments we explore the incremental unknowns method; linear stationary as well as evolutionary problems are considered. For linear stationary problems, the method appears as a nearly optimal two-step preconditioning technique. At each step, we observe that the convergence behavior of the iterative methods employed is dramatically different, depending upon whether or not preconditioning is used. For linear evolutionary problems, successful and sharply accurate long-term integration is observed when the incremental unknowns (other than that of the coarsest level) are, effectively, small quantities. Otherwise, systematical aliasing arises. © 1994 John Wiley & Sons, Inc.     

Numerical method for estimating multivariate conditional distributions

Summary  A computational framework for estimation of multivariate conditional distributions is presented. It allows the forecast of the joint distribution of target variables in dependence on explaining variables. The concept can be applied to general distribution families such as stable or hyperbolic distributions. The estimation is based on the numerical minimization of the cross entropy, using the Multi-Level Single-Linkage global optimization method. Nonlinear dependencies of conditional parameters can be modeled with help of general functional approximators such as multi-layer perceptrons. In applications, the information about a complete distribution of forecasts can be used to quantify the reliability of the forecast or for decision support. This is illustrated on a case study concerning the spare parts demand forecast. The improvement of the forecast error due to using non-Gaussian distributions is presented in another case study concerning the truck sales forecast.     

New general guidance method in constrained optimal control,part 1: Numerical method

A very fast numerical method is developed for the computation of neighboring optimum feedback controls. This method is applicable to a general class of optimal control problems (for example, problems including inequality constraints and discontinuities) and needs no on-line computation, except for one matrix-vector multiplication. The method is based on the so-called accessory minimum problem. The necessary conditions for this auxiliary optimal control problem form a linear multipoint boundary-value problem with linear jump conditions, which is especially well suited for numerical treatment. In the second part of this paper, the performance of the guidance scheme is shown for the heating-constrained cross-range maximization problem of a space-shuttle-orbiter-type vehicle.This research was supported in part by the Deutsche Forschungsgemeinschaft under the Schwerpunktprogramm Anwendungsbezogene Optimierung und Steuerung.The authors wish to express their sincere and grateful appreciation to Professor Roland Bulirsch who encouraged this work.     

Numerical grid generator based on Moser's deformation method

A deformation method of grid generation has been recently proposed. The method is based on Moser's deformation scheme in his study of the volume elements of a Riemannian manifold. In this paper, this deformation method is improved so that the grid adaption takes place according to the physical coordinates. Some numerical results are included to demonstrate the method. © 1994 John Wiley & Sons, Inc.     

Numerical indefinite integration by double exponential sinc method

We present a numerical method for approximating an indefinite integral by the double exponential sinc method. The approximation error of the proposed method with integrand function evaluations is

for a reasonably wide class of integrands, including those with endpoint singularities. The proposed method compares favorably with the existing formulas based on the ordinary sinc method. Computational results show the accordance of the actual convergence rates with the theoretical estimate.

     

Numerical optimization method for packing regular convex polygons

An algorithm is presented for the approximate solution of the problem of packing regular convex polygons in a given closed bounded domain G so as to maximize the total area of the packed figures. On G a grid is constructed whose nodes generate a finite set W on G, and the centers of the figures to be packed can be placed only at some points of W. The problem of packing these figures with centers in W is reduced to a 0-1 linear programming problem. A two-stage algorithm for solving the resulting problems is proposed. The algorithm finds packings of the indicated figures in an arbitrary closed bounded domain on the plane. Numerical results are presented that demonstrate the effectiveness of the method.     

Numerical stability of one method of asymptotic stabilization

A problem of numerical projection onto a stable manifold in a neighborhood of a fixed point of hyperbolic type is considered. It is shown that a nonlinear iterative method of projection construction is stable with respect to errors occurring in solutions of intermediate problems. A formulation of the corresponding assertion and results of numerical simulations for solution of the problem on asymptotic stabilization over initial data for an equation of barotropic vortex type on a semisphere are presented.     

Numerical study of fisher's equation by Adomian's method

The effect of the linear operator L, used in the Adomian's method for solving nonlinear partial differential equations, on the convergence is studied on the Fisher's equation, which describes a balance between linear diffusion and nonlinear reaction. The results show that the convergence of this method is not influenced by the choice of the operator L in the equation to be solved. Furthermore, under some conditions, these results are close to those obtained by using other numerical techniques.     

Numerical method for generalized time fractional KdV-type equation

In this article, an efficient numerical method for linearized and nonlinear generalized time-fractional KdV-type equations is proposed by combining the finite difference scheme and Petrov–Galerkin spectral method. The scale and weight functions involved in generalized fractional derivative cause too much difficulty in discretization and numerical analysis. Fortunately, motivated by finite difference method for fractional differential equation on graded mesh, the stability and convergence of the constructed method are established rigorously. It is proved that the full discretization schemes of generalized time-fractional KdV-type equation is unconditionally stable in linear case. While for nonlinear case, it is stable under a CFL condition and for not small ϵ, coefficient of the high-order spatial differential term. In addition, the full discretization schemes with respect to linear and nonlinear cases respectively converge to the associated exact solutions with orders and , where τ, α, N and m accordingly indicate the time step size, the order of the fractional derivative, polynomial degree, and regularity of the exact solution. Numerical experiments are carried out to support the theoretical results.