No description available.

<p>This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov type) as well as a tted operator nite di erence method. We notice that results on Bakhvalov mesh are better than those on Shishkin mesh. However, piecewise uniform meshes provide a simpler platform for analysis and computations. Fitted operator methods are even simpler in these regards due to the ease of operating on uniform meshes. Richardson extrapolation is applied on one of the tted mesh nite di erence method (those based on Shishkin mesh) as well as on the tted operator nite di erence method in order to improve the accuracy and/or the order of convergence. This is our main contribution to this eld and in fact we have achieved very good results after extrapolation on the tted operator finitete difference method. Extensive numerical computations are carried out on to confirm the theoretical results.</p>

Thesis (M.S)--Ohio University, March, 2005. / Includes bibliographical references (p. 44-45)

Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010. / Committee Chair: Pan, Ronghua; Committee Member: Chow, Shui-Nee; Committee Member: Dieci, Luca; Committee Member: Gangbo, Wilfrid; Committee Member: Yeung, Pui-Kuen. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (M.Sc. (Dept. of Mathematics, Faculty of Natural Sciences))--University of the Western Cape, 2009. / Bibliography: leaves 180-195.

Thesis (M.S)--Ohio University, March, 2005. / Title from PDF t.p. Includes bibliographical references (p. 44-45)

Magister Scientiae - MSc / This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov type) as well as a tted operator nite di erence method. We notice that results on Bakhvalov mesh are better than those on Shishkin mesh. However, piecewise uniform meshes provide a simpler platform for analysis and computations. Fitted operator methods are even simpler in these regards due to the ease of operating on uniform meshes. Richardson extrapolation is applied on one of the tted mesh nite di erence method (those based on Shishkin mesh) as well as on the tted operator nite di erence method in order to improve the accuracy and/or the order of convergence. This is our main contribution to this eld and in fact we have achieved very good results after extrapolation on the tted operator finitete difference method. Extensive numerical computations are carried out on to confirm the theoretical results. / South Africa

Numerical relativity is concerned with the generation of solutions to Einstein's equations by numerical means. In general, the construction of such a spacetime is accomplished in two stages: 1) the determination of initial data which is specified on a single spacelike hypersurface and satisfies four initial value equations, and 2) the evolution of the initial data to generate the spacetime or some portion of it. One of the key problems is the development of efficient algorithms for the solutions of these equations, as they are sufficiently complex to tax the fastest present computers. This thesis presents a comparison of various algorithms for the solution of the initial value equations, concentrating on the recently developed multi-grid method. The specific problem examined has been previously studied by Bowen, Piran and York. Their initial data has been interpreted as representing "snapshots" of three new families of black holes. Three of the four initial value equations possess analytic solutions. The remaining 2-dimensional nonlinear partial differential equation is solved numerically in this thesis using finite difference techniques. The performance of the multi-grid method, with respect to three more well-known methods, is evaluated through numerical experiments. The speed and reliability of the multi-grid algorithm are found to be very good. In addition, the results which had been previously calculated numerically by Piran are essentially reproduced, with the correction of some errors in that work. Possible extensions of the work to more complex initial value problems are also discussed. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The solution of initial value problems (IVPs) provides the evolution of dynamic system state history for given initial conditions. Solving boundary value problems (BVPs) requires finding the system behavior where elements of the states are defined at different times. This dissertation presents a unified framework that applies modified Chebyshev-Picard iteration (MCPI) methods for solving both IVPs and BVPs. Existing methods for solving IVPs and BVPs have not been very successful in exploiting parallel computation architectures. One important reason is that most of the integration methods implemented on parallel machines are only modified versions of forward integration approaches, which are typically poorly suited for parallel computation. The proposed MCPI methods are inherently parallel algorithms. Using Chebyshev polynomials, it is straightforward to distribute the computation of force functions and polynomial coefficients to different processors. Combining Chebyshev polynomials with Picard iteration, MCPI methods iteratively refine estimates of the solutions until the iteration converges. The developed vector-matrix form makes MCPI methods computationally efficient. The power of MCPI methods for solving IVPs is illustrated through a small perturbation from the sinusoid motion problem and satellite motion propagation problems. Compared with a Runge-Kutta 4-5 forward integration method implemented in MATLAB, MCPI methods generate solutions with better accuracy as well as orders of magnitude speedups, prior to parallel implementation. Modifying the algorithm to do double integration for second order systems, and using orthogonal polynomials to approximate position states lead to additional speedups. Finally, introducing perturbation motions relative to a reference motion results in further speedups. The advantages of using MCPI methods to solve BVPs are demonstrated by addressing the classical Lambert’s problem and an optimal trajectory design problem. MCPI methods generate solutions that satisfy both dynamic equation constraints and boundary conditions with high accuracy. Although the convergence of MCPI methods in solving BVPs is not guaranteed, using the proposed nonlinear transformations, linearization approach, or correction control methods enlarge the convergence domain. Parallel realization of MCPI methods is implemented using a graphics card that provides a parallel computation architecture. The benefit from the parallel implementation is demonstrated using several example problems. Larger speedups are achieved when either force functions become more complicated or higher order polynomials are used to approximate the solutions.

Syfte: Genom att i praktiken se hur företag identifierar immateriella tillgångar syftar den här studien att ur ett intressentperspektiv diskutera relevansen, tillförlitligheten och jämförbarheten av det initiala värdet av goodwill.Metod: Studien baseras på en kvalitativ fenomenografisk metodansats. Djupintervjuer och telefonintervjuer har används för att samla in det empiriska materialet. Empirin har därefter behandlats med en abduktionsansats för att möjliggöra en diskussion genom att pendla mellan det empiriska materialet och tänkbara teorier.Analys: Utifrån legitimitet- och intressentteorin kan skillnaderna i redovisningen förklaras av: 1) Företagsledares tolkning av det sociala kontraktet. 2) IFRS. 3) Revisorns roll. 4) Intressenternas makt, legitimitet och brådska. 5) Börsnoterat kontra icke börsnoterat.Slutsats: Studien finner att IFRS 3 inte ökar relevansen, tillförlitligheten och jämförbarheten av informationen förvärvaren ger om det förvärvade bolaget. För att IFRS 3 ska uppnå syftet med relevans, tillförlitlighet och jämförbarhet, bör de införas en tydlig vägledning hur företagen ska identifiera och värdera immateriella tillgångar efter ett rörelseförvärv. Vidare forskning krävs för att fastställa vilka egenskaper identifierbara tillgångar och goodwill besitter. / This thesis is written in Swedish.Purpose: The purpose of this thesis is through practice see how companies identifies intangible assets and by using a stakeholder perspective discuss the relevance, reliability and comparability of the initial value of goodwill.Methodology: This thesis is based on a qualitative phenomenography methodology. The empirical material have been gathered through in-depth interviews and telephone interviews. An abductive approach where applied on the empirical data and selective theories to enhance the discussion.Analysis: By applying the legitimacy and stakeholder theory the de facto difference in the accounting of the initial value of goodwill can be explained by: 1) Managers interpretation of the social contract. 2) IFRS. 3) The role of the accountant. 4) Power, legitimacy and urgency of the stakeholder. 6) Publicly listed company vs. unlisted company.Findings: This thesis finds that IFRS 3 do not increase the relevance, reliability and comparability of the information the acquirer discloses of the acquired company. If IFRS 3 is to fulfill its purpose of relevance, reliability and comparability, IASB needs to introduce a guidance how companies should identify and appraise intangible assets after acquisitions. Further research is needed on what properties intangible assets have and how goodwill should properly be classified.