Validated Numerical Bounds on the Global Error for Initial Value Problems for Stiff Ordinary Differential Equations Chao Yu Master of Science Graduate Department of Computer Science University of Toronto 2004 There are many standard numerical methods for initial value problems (IVPs) for ordinary differential equations (ODEs). Compared with these methods, validated methods for IVPs for ODEs pro...

"In this paper we investigate the existence of solutions initial value problems (IVP for short), partial hyperbolic functional and neutral differential inclusions fractional order involving Caputo derivative with finite delay by using nonlinear alternative Frigon type multivalued admissible contraction in Frechet spaces."

The article proves the existence of a maximum of two possible solutions to the initial value problem composed by the planar-perspective equation and an initial condition. This initial value problem has a geometric interpretation. Solutions are curves than pass trough the initial condition which is point of the plane. 1 Description of the problem Let C be a regular curve in the plane R parameter...

In this paper, we show that there are Initial Value Problems defined with polynomial ordinary differential equations that can simulate universal Turing machines in the presence of bounded noise. The polynomial ODE defining the IVP is explicitly obtained and the simulation is performed in real time.

Chemical processes are modeled by large-scale, highly-nonlinear process models often governed by unstable dynamics. Dynamic optimization is required to exploit economical performance of these processes in their unstable regions. On the one hand, direct single shooting is able to solve large-scale dynamic optimization problems, but lacks the ability to cope properly with unstable dynamical syste...

Equations of Hamilton-Jacobi type arise in many areas of application, including the calculus of variations, control theory and differential games. The associated initial-value problems almost never have global-time classical solutions, and one must deal with suitable generalized solutions. The correct class of generalized solutions has only recently been established by the authors. This article...

‎‎in this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎the solutions of fractional difference equation are the size of tumor in model tumor growth described by the gompertz f...

A total of 120 barrows (initial BW = 47.9 ± 3.6 kg; PIC 1050) were used in an 83-d study to determine the effects of dietary iodine value (IV) product (IVP) on growth performance and fat quality. Pigs were blocked by BW and randomly allotted to 1 of 6 treatments with 2 pigs per pen and 10 pens per treatment. Dietary treatments were fed in 3 phases and formulated to 3 IVP concentrations (low, me...