Foreign Ownership Restrictions: A Numerical Approach

In this paper, we analyze the reason behind the use of foreign ownership restrictions on inward Foreign Direct Investment (FDI). We extend the results developed in Karabay (2005) by changing the condition on share distribution in the model. Due to this change, we are able to analyze the political economy aspect of this restrictive policy, i.e., we can study the effect of the host government’s welfare preference on the optimal foreign ownership restriction. Since the analytical solution to the optimal share restriction policy cannot be specified in general, we use a numerical approach based on collocation to approximate the solution to the problem. Within this framework, under certain conditions, it turns out that the rent extraction-efficiency trade-off is sharper the less the host government favors the local firm. We show that not only economic factors but also political factors play an important role in the determination of the foreign ownership restrictions. The views expressed in this paper are those of the authors and are not necessarily reflective of views of the Central Bank of the Republic of Turkey. All errors are our own.     

A Posteriori Error Estimates for Parabolic Variational Inequalities

We study a posteriori error estimates in the energy norm for some parabolic obstacle problems discretized with a Euler implicit time scheme combined with a finite element spatial approximation. We discuss the reliability and efficiency of the error indicators, as well as their localization properties. Apart from the obstacle resolution, the error indicators vanish in the so-called full contact set. The case when the obstacle is piecewise affine is studied before the general case. Numerical examples are given.     

Numerical Solution of a Reaction-Diffusion Elliptic Interface Problem with Strong Anisotropy

We consider a singularly perturbed reaction-diffusion elliptic problem in two dimensions (x,y), with strongly anisotropic coefficients and line interface. The second order derivative with respect to x is multiplied by a small parameter ². We construct finite volume difference schemes on condensed Shihskin meshes and prove -uniform convergence in discrete energy and maximum norms. Numerical experiments that agree with the theoretical results are given.     

Initialisation of the adaptive Huber method for solving the first kind Abel integral equation

In the previous work of this author (Bieniasz in Computing 83:25–39, 2008) an adaptive numerical method for solving the first kind Abel integral equation was described. It was assumed that the starting value of the solution was known and equal zero. This is a frequent situation in some applications of the Abel equation (for example in electrochemistry), but in general the starting solution value is unknown and non-zero. The presently described extension of the method allows one to automatically determine both the starting solution value and the estimate of its discretisation error. This enables an adaptive adjustment of the first integration step, to achieve a pre-defined accuracy of the starting solution. The procedure works most satisfactorily in cases when the solution possesses all, or at least several of the lowest, derivatives at the initial value of the independent variable. Otherwise, a discrepancy between the true and estimated errors of the starting solution value may occur. In such cases one may either start integration with as small step as possible, or use a smaller error tolerance at the first step.      

An adaptive Huber method with local error control,for the numerical solution of the first kind Abel integral equations

In contrast to the existing plethora of adaptive numerical methods for differential and integro-differential equations, there seems to be a shortage of adaptive methods for purely integral equations with weakly singular kernels, such as the first kind Abel equation. In order to make up this deficiency, an adaptive procedure based on the product-integration method of Huber is developed in this work. In the procedure, an a posteriori estimate of the dominant expansion term of the local discretisation error at a given grid node is used to determine the size of the next integration step, in a way similar to the adaptive solvers for ordinary differential equations. Computational experiments indicate that in practice the control of the local errors is sufficient for bringing the true global errors down to the level of a prescribed error tolerance. The lower limit of the acceptable values of the error tolerance parameter depends on the interference of machine errors, and the quality of the approximations available for the method coefficients specific for a given kernel function.      

Maximum a posteriori parameter estimation in large-scale systems

In this paper we examine the use of the maximum a posteriori (MAP) approach for parameter estimation in large-scale interconnected dynamical systems. We examine both the suboptimal approach of Sage and the optimal approaches which arise on solving within a multi-level structure the resulting nonlinear two point boundary value problem. In particular we consider two optimal methods i.e. the costate prediction method and the state estimation approach of Chen and Perlis as applied to parameter estimation. We illustrate the approaches on a simple example which is used as a bench mark problem for purposes of comparison of the numerical efficiency of the various techniques.     

Numerical Convergence of a Parameterisation Method for the Solution of a Highly Anisotropic Two-Dimensional Elliptic Problem

Highly anisotropic two-dimensional elliptic problems lead to severe numerical difficulties. In this paper, starting from a simple finite volume scheme, we present a parameterisation method that allows us to obtain the solution even if the anisotropy ratio is very large. We derive a formal asymptotic limit of the two-dimensional anisotropic problem, in the case where the anisotropy ratio goes to infinity. This formal limit is used as a reference, and we show that the parameterisation method gives similar results, whereas the finite volume scheme fails to give an accurate solution. Numerical results are given, which indicate important parameters to be considered in order to obtain a good precision     

Numerical solution of singularly perturbed two point boundary value problems by spline in compression

Some difference schemes for singularly perturbed two point boundary value problems are derived using spline in compression. These schemes are second order accurate. Numerical examples are given in support of the theoretical results.     

Numerical computation of the eigenvalues of a discontinuous Dirac system using the sinc method with error analysis

In this paper, we apply a regularized sinc method to compute the eigenvalues of a discontinuous regular Dirac system with transmission conditions at the point of discontinuity. The regularized technique allows us to insert some parameters to the well-known sinc method, strengthening the existing technique, and to avoid the aliasing error. The error analysis is established considering both the truncation and amplitude errors associated with the sampling theorem. Numerical examples together with tables and illustrative figures are given.     

Some Modified Runge-Kutta Methods for the Numerical Solution of Initial-Value Problems with Oscillating Solutions

Two new modified Runge-Kutta methods with minimal phase-lag are developed for the numerical solution of initial-value problems with oscillating solutions which can be analyzed to a system of first order ordinary differential equations. These methods are based on the well known Runge-Kutta RK5(4)7FEq1 method of Higham and Hall (1990) of order five. Also, based on the property of the phase-lag a new error control procedure is introduced. Numerical and theoretical results show that this new approach is more efficient compared with the well known Runge-Kutta Dormand-Prince RK5(4)7S method [see Dormand and Prince (1980)] and the well known Runge-Kutta RK5(4)7FEq1 method of Higham and Hall (1990).     

Parallel algorithms for the solution of certain large sparse linear systems

A couple of approximate inversion techniques are presented which provide a parallel enhancement to several iterative methods for solving linear systems arising from the discretization of boundary value problems. In particular, the Jacobi, Gauss‐Seidel, and successive overrelaxation methods can be improved substantially in a parallel environment by the extensions considered. A special case convergence proof is presented. The use of our approximate inverses with the preconditioned conjugate gradient method is examined and comparisons are made with some recently proposed algorithms in this area that also employ approximate inverses. The methods considered are compared under sequential and parallel hardware assumptions.     

Application of a Numerical Increased-Accuracy Method to the Solution of a Heat Transfer Equation

Based on the Hermite formula, a numerical method for solution of a heat transfer equation is described. Expressions are given for computation of the coefficients of the Hermite formula from free parameters. The use of the method is illustrated by an example of solution of a model problem.     

Simple a posteriori error estimators for the <Emphasis Type="Italic">h</Emphasis>-version of the boundary element method

The h-h/2-strategy is one well-known technique for the a posteriori error estimation for Galerkin discretizations of energy minimization problems. One considers to estimate the error , where is a Galerkin solution with respect to a mesh and is a Galerkin solution with respect to the mesh obtained from a uniform refinement of . This error estimator is always efficient and observed to be also reliable in practice. However, for boundary element methods, the energy norm is non-local and thus the error estimator η does not provide information for a local mesh-refinement. We consider Symm’s integral equation of the first kind, where the energy space is the negative-order Sobolev space . Recent localization techniques allow to replace the energy norm in this case by some weighted L ²-norm. Then, this very basic error estimation strategy is also applicable to steer an h-adaptive algorithm. Numerical experiments in 2D and 3D show that the proposed method works well in practice. A short conclusion is concerned with other integral equations, e.g., the hypersingular case with energy space and , respectively, or a transmission problem. Dedicated to Professor Ernst P. Stephan on the occasion of his 60th birthday.     

An adaptive wavelet collocation method for solving optimal control of elliptic variational inequalities of the obstacle type

This paper presents a fast computational technique based on the wavelet collocation method for the numerical solution of an optimal control problem governed by elliptic variational inequalities of obstacle type. In this problem, the solution divides the domain into contact and noncontact sets. The boundary between the contact and noncontact sets is a free boundary, which is not known a priori and the solution is not smooth on it. Accordingly, a very fine grid is needed in order to obtain a solution with a reasonable accuracy. In this paper, our aim is to propose an adaptive scheme in order to generate an appropriate and economic irregular dyadic mesh for finding the optimal control and state functions. The irregular mesh will be generated such that its density around the free boundary is higher than in other places and high-resolution computations are focused on these zones. To this aim, we use an adaptive wavelet collocation method and take advantage of the fast wavelet transform of compact-supported interpolating wavelets to develop a multi-level algorithm, which generates an adaptive computational grid. Using this adaptive grid takes less CPU time than using a full regular mesh. At each step of the algorithm, the active set method is used for solving the optimality system of the obstacle problem on the adapted mesh. Finally, the numerical examples are presented to show the validity and efficiency of the technique.     

Adaptive control of service in queueing systems

We consider the service-rate selection problem in an M/G/1 queueing system with unknown arrival rate and average cost criterion. An optimal adaptive policy is determined using recently developed results on parameter estimation and adaptive control of semi-Markov processes.     

Integrating load balancing and locality in the parallelization of irregular problems

An irregular problem models the evolution of a system where several elements are irregularly distributed in a domain. The evolution modifies this distribution in a way that cannot be foreseen and the behavior of each element depends upon the elements close to it according to a problem dependent relation. Starting from a hierarchical representation of the domain, we define a parallelization methodology that includes a load balancing strategy that preserves this locality property and a strategy to collect information distributed onto the processing nodes.