Issued also as Thesis (Ph. D.)--Columbia University. / Bibliography: p. 58.

Thesis--Copenhagen. / "Litteraturfortegnelse": p. [109]-110.

Thesis (Ph.D.) -- University of Rhode Island, 2009. / Typescript. Includes bibliographical references (leaves 62-64).

Thesis (Ph.D.) -- University of Rhode Island, 2009. / Typescript. Includes bibliographical references (leaves 108-111).

Thesis (Ph. D.)--Catholic University of America, 1936. / Vita. Bibliography: p. 160-165.

Thesis (Ph. D.)--University of Rhode Island, 2005. / Typescript. Includes bibliographical references (leaves 55-57).

Thesis (Ph. D.)--University of Rhode Island, 2006. / Includes bibliographical references (leaves 175-178).

Finite difference numerical methods are developed for the solution system in the biomedical sciences; namely, fox-rabies model. First-order methods and second-order method are developed to solve the fox-rabies equations. The fox-rabies model is extended to one-space dimension to incorporate diffusion. The reaction terms in these systems of partial differential equations contain non-linear expressions. It is seen that the numerical solutions are obtained by solving non-linear algebraic system at each time step, as opposed to solving anon-linear algebraic system which is often required when integrating non-linear partial differential equations. The numerical methods proposed for the solution of the initial-value problem for the fox-rabies model are characterized to be implicit. In each case, however, it seen that the numerical solutions are obtained explicitly. In a series of numerical experiments, in which the ordinary differential equations are solved first of all, it seen that the proposed methods have an identical stability properties to those of the well-known, first-order, Euler method. The proposed methods for the numerical solution of partial differential equations are seen to be economical and reliable. Error analysis for the methods, computer implementation and numerical results are discussed. The stability of the numerical method is analyzed using maximum principle analysis.

Syftet med denna undersökning är att analysera eventuella löne- och sysselsättningseffekter generade av återinförandet av ROT-avdraget 2008. Återinförandet sågs som en permanent åtgärd med målet att motverka så kallade svartarbeten och öka byggandet i Sverige. Vi vill med denna undersökning utvärdera vilka löne- och sysselsättningseffekter som ROT-avdraget bidragit till. En difference-in-difference metod kommer att användas för att analysera data insamlade från aktiebolag i Sverige, aggregerat till branschnivå. Aggregeringen görs för att våra resultat skall vara direkt jämförbara med tidigare studier, samt för att inte exkludera den effekt som orsakas av att nya företag i dessa branscher kan ha startats på grund av reformen. Difference-in-difference metoden går ut på att en behandlad grupp bestående av de byggbranscher som påverkats av ROT-avdragets införande jämförs med en kontrollgrupp bestående av övriga branscher före och efter reformen. Våra resultat visar att den genomsnittliga lönesumman per anställd inte påverkats av reformen, medan reformen givit en ökning i det genomsnittliga antalet anställda i ROT-branscherna. / The purpose of this paper is to analyze the possible wage and employment effects generated by the reintroduction of the ROT-deduction in 2008. The reintroduction was seen as a permanent measure, and the aim was to counteract undeclared work and to stimulate and increase the building in Sweden. With this paper, we want to evaluate the wage and employment effects that the ROT-deduction contributed to in Swedish construction companies, more specifically limited companies in the ROT industry. A difference-in-difference method will be used to analyze data collected from limited companies in Sweden, aggregated to industry level. Aggregation is made for our results to be directly comparable to previous studies, and to not exclude the effect caused by new companies in the ROT-industry that may have started due to the reform. The difference-in-difference method involves that a treated group consisting of the construction industries affected by the introduction of the ROT-deduction is compared to a control group consisting of other industries before and after the reform. Our results show that the average wage per employee is not affected by the reform, while the reform has increased the average number of employees in the ROT-industry.

The first chapter of the thesis is concerned with the construction of finite difference approximations to boundary value problems in linear nth order ordinary differential equations. This construction is based upon a local collocation procedure with polynomials, which is equivalent to a method of undetermined coefficients. It is shown that the coefficients of these finite difference approximations can be expressed as the determinants of matrices of relatively small dimension. A basic theorem states that these approximations are consistent, provided only that a certain normalization factor does not vanish. This is the case for compact difference equations and for difference equations with only one collocation point. The order of consistency may be improved by suitable choice of the collocation points. Several examples of known, as well as new difference approximations are given. Approximations to boundary conditions are also treated in detail. The stability theory of H. O. Kreiss is applied to investigate the stability of finite difference schemes based upon these approximations. A number of numerical examples are also given. In the second chapter it is shown how the construction method of the first chapter can be extended to initial value problems for systems of linear first order ordinary differential equations. Specific examples are 'included and the well-known stability theory for these difference equations is summarized. It is then shown how these difference methods may be applied to linear parabolic partial differential equations in one space variable after first discretizing in space by a suitable method from the first chapter. The stability of such difference schemes for parabolic equations is investigated using an eigenvalue-eigenvector analysis. In particular, the effect of various approximations to the boundary conditions is considered. The relation of this analysis to the stability theory of J. M. Varah is indicated. Numerical examples are also included. / Science, Faculty of / Mathematics, Department of / Graduate