No description available.

No description available.

Although one significant method of interpolation is that of the cubic spline, it has the drawback of occasionally producing undesired inflections in a curve. As a remedy, the spline can mathematically be "stretched" (so to speak) in much the same way that a draftsman's spline could be pulled at its ends while still being anchored at certain points throughout.This thesis will make use of FORTRAN subroutines given in the April, 1974 issue of Communications of the ACM, which have the capability of applying this tension factor to a cublic spline in a graphics package. It will also discuss the necessary modifications which are required before compatibility can be achieved between these subroutines and the Tektronix terminal which is coupled to the DEC-10 here at Ball State University.

Fragmentation equations occur naturally in many real world problems, see [ZM85, ZM86, HEL91, CEH91, HGEL96, SLLM00, Ban02, BL03, Ban04, BA06] and references therein. Mathematical study of these equations is mostly concentrated on building existence and uniqueness theories and on qualitative analysis of solutions (shattering), some effort has be done in finding solutions analytically. In this project, we deal with numerical analysis of fragmentation equation with transport. First, we provide some existence results in Banach and Hilbert settings, then we turn to numerical analysis. For this approximation and interpolation theory for generalized Laguerre functions is derived. Using these results we formulate Laguerre pseudospectral method and provide its stability and convergence analysis. The project is concluded with several numerical experiments. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2012.

Bibliography: leaves 77-78 / 78 leaves : ill. (some col.) ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1986

John N. Tsitsiklis, Bernard C. Levy. / Bibliography: leaves 18-19. / "December, 1981." / "National Science Foundation ... Grant ECS-80-12668"

by Thomas Mac Athay. / Bibliography: p.109-111. / Prepared under grant ERDA-E(49-18)-2087. Originally presented as the author's thesis, (M.S. and E.E.), M.I.T. Dept. of Electrical Engineering and Computer Science, 1976.

No description available.

The concept of backward stochastic differential equation (BSDE) was initially brought up by Bismut when studying the stochastic optimal control problem. And it has been applied to describe various problems particularly to those in finance. After the fundamental work by Pardoux and Peng who proved the well-posedness of the nonlinear BSDE, the BSDE has been investigated intensively for both theoretical and practical purposes. In this thesis, we are concerned with a class of numerical methods for solving BSDEs, especially the one proposed by Zhao et al.. For this method, the convergence theory of the semi-discrete scheme (the scheme that discretizes the equation only in time) was already established, we shall further provide the analysis for the fully discrete scheme (the scheme that discretizes in both time and space). Moreover, using the BSDE as the adjoint equation, we shall construct the numerical method for solving the stochastic optimal control problem. We will discuss the situation when the control is deterministic as well as when the control is feedback.

The numerical solutions of many types of problems are generally obtained by solving approximating linear algebraic systems. Moreover, in solving a nonlinear problem, one may replace it by a sequence of linear systems providing progressively improved approximations. For the study of these linear systems of equations a geometric terminology with the compact symbolism of vectors and matrices is useful. A resume of the basic principles of higher algebra necessary for the development of the material to follow is therefore included. / "A Paper." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Paul J. McCarthy, Professor Directing Paper. / "May, 1958." / At head of title: Florida State University. / Typescript. / Includes bibliographical references.