Combining make to order and make to stock

In inventory control and production planning one is tempted to use one of two strategies: produce all demand to stock or produce all demand to order. The disadvantages are well-known. In the make everything to order case (MTO) the response times may become quite long if the load is high, in the make everything to stock case (MTS) one gets an enormous inventory if the number of different products is large.In this paper we study two simple models which combine MTO and MTS, and investigate the effect of combining MTO and MTS on the production lead times.     

An efficient Chebyshev-Tau spectral method for Ginzburg-Landau-Schrödinger equations

We propose an efficient time-splitting Chebyshev-Tau spectral method for the Ginzburg-Landau-Schrödinger equation with zero/nonzero far-field boundary conditions. The key technique that we apply is splitting the Ginzburg-Landau-Schrödinger equation in time into two parts, a nonlinear equation and a linear equation. The nonlinear equation is solved exactly; while the linear equation in one dimension is solved with Chebyshev-Tau spectral discretization in space and Crank-Nicolson method in time. The associated discretized system can be solved very efficiently since they can be decoupled into two systems, one for the odd coefficients, the other for the even coefficients. The associated matrices have a quasi-tridiagonal structure which allows a direction solution to be obtained. The computation cost of the method in one dimension is O(Nlog(N)) compared with that of the non-optimized one, which is O(N²). By applying the alternating direction implicit (ADI) technique, we extend this efficient method to solve the Ginzburg-Landau-Schrödinger equation both in two dimensions and in three dimensions, respectively. Numerical accuracy tests of the method in one dimension, two dimensions and three dimensions are presented. Application of the method to study the semi-classical limits of Ginzburg-Landau-Schrödinger equation in one dimension and the two-dimensional quantized vortex dynamics in the Ginzburg-Landau-Schrödinger equation are also presented.     

A second-order analytic solution for oscillatory wind-induced flow in an idealized shallow lake

We present a second-order analytic solution to the nonlinear depth-integrated shallow water equations for free-surface oscillatory wind-driven flow in an idealized lake. Expressing the solution as an asymptotic expansion in the dimensionless wave amplitude (ζ/h), which is considered to be a small parameter, enables simplification of the governing equations and permits the use of a perturbation approach to solve them.This analytic solution provides a benchmark for testing numerical models. In particular, the main merit of this solution is that it accounts for advective effects, which are typically omitted from analytic solutions of two-dimensional free surface flow. In order to retain these effects in an analytic solution, we restrict our attention to forcing from a monochromatic wind stress, consider a constant depth rectangular lake, and simplify the governing equations by omitting the Coriolis and eddy viscosity terms and using a linearised friction factor. As such, the analytic solution is of limited use for considering real world problems. Due to the complexity of the analytic solution computer code for this solution is available online.Our solution is valid for cases where changes in the water surface level are small compared with the depth of the lake, and the advective terms in the momentum equations are small compared with acceleration terms. We examine the validity of these assumptions for three test cases, and compare the second-order analytic solution to numerical results to verify an existing hydrodynamic model.     

Asymptotic stability of block boundary value methods for delay differential-algebraic equations

Block boundary value methods are applied to solve a class of delay differential-algebraic equations. We focus on the asymptotic stability of the numerical methods for linear delay differential-algebraic equations with multiple delays. It is shown that A-stable block boundary value methods satisfying a restrictive condition can preserve the asymptotic stability of the analytical solution. Numerical experiments further confirm the effectiveness and stability of the methods.     

An efficient multigrid preconditioner for Maxwell’s equations in micromagnetism

We consider a system of Maxwell’s and Landau-Lifshitz-Gilbert equations describing magnetization dynamics in micromagnetism. The problem is discretized by a convergent, unconditionally stable finite element method. A multigrid preconditioned Uzawa type method for the solution of the algebraic system resulting from the discretized Maxwell’s equations is constructed. The efficiency of the method is demonstrated on numerical experiments and the results are compared to those obtained by simplified models.     

Linear complete differential resultants and the implicitization of linear DPPEs

The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of n$n$ linear differential polynomial parametric equations in n−1$n-1$ differential parameters. We give necessary conditions to ensure properness of the system of differential polynomial parametric equations.     

非线性延迟积分微分方程单支方法的散逸性

本文研究了非线性延迟积分微分方程单支方法的散逸性．把G（c3P30）-代数稳定的单支方法应用到以上方程中,得到了在有限维空间和无限维空间的散逸性结果．文章最后,数值试验验证了本文的结论．     

Anti-periodic fractional boundary value problems

We study a class of anti-periodic boundary value problems of fractional differential equations. Some existence and uniqueness results are obtained by applying some standard fixed point principles. Several examples are given to illustrate the results.     

On global solutions to fractional functional differential equations with infinite delay in Fréchet spaces

In this paper, we investigate global uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces. We shall rely on a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to Frigon and Granas. The results are obtained by using the α-resolvent family (S_α(t))_t≥0 on a complex Banach space X combined with the above-mentioned fixed point theorem. As an application, a controllability result with one parameter is also provided to illustrate the theory.     

Iterative methods for solving extended general mixed variational inequalities

In this paper, we introduce and consider a new class of mixed variational inequalities involving four operators, which are called extended general mixed variational inequalities. Using the resolvent operator technique, we establish the equivalence between the extended general mixed variational inequalities and fixed point problems as well as resolvent equations. We use this alternative equivalent formulation to suggest and analyze some iterative methods for solving general mixed variational inequalities. We study the convergence criteria for the suggested iterative methods under suitable conditions. Our methods of proof are very simple as compared with other techniques. The results proved in this paper may be viewed as refinements and important generalizations of the previous known results.