ABSTRACTQIANG SHI. A convertible-bond-pricing method based on bond prices on markets.(Under the direction of DR. YOU-LAN ZHU)This thesis is devoted to evaluating two-factor convertible bonds. Different zero-coupon bond curves are inputted when eva...
We present a new algorithm for approximating solutions of two-point boundary value problems and prove theorems that give conditions under which the solution must exist and the algorithm generate approximations that converge to it. We show how to m...
An inverse problem of the determination of an initial condition in ahyperbolic equation from the lateral Cauchy data is considered. Thisproblem has applications to the thermoacoustic tomography, as wellas to linearized coefficient inverse problems...
Fluid instabilities, particularly interfacial instabilities, have proven to be a powerful mechanism in driving and sustaining combustion processes in several devices of practical interest. Modern combustors are in fact designed to exploit the mixi...
The design basis functions in IGA are refined and enhanced by extra enrichment functions and various local refinements with the use of partition of unity (PU) functions with flat-top. These reconditioned and modified basis functions are pushed for...
We develop numerical methods for analysis of fourth-order partial differential equations on domains with angular corners. For the finite element analysis of fourth-order partial differential equations, we have to use smoother basis functions whose...
Computing turbulent flow is very difficult but forms the basis for computational experiments in Meteorology and Oceanography. To overcome the difficulty and complexity in turbulence computation, a spectrally hyperviscous version of Navier-Stokes e...
This dissertation is mainly a study of the center problem in the context of a family of three dimensional systems of ordinary differential equations of the form· {u} = &minus v + P(u,v,w), · {v} = u+Q(u,v,w), · {w}=&minus &lambda...
