Discontinuous Quantum Stochastic Differential Equations and The Associated Kurzweil Equations

Quantum stochastic differential equations (QSDEs) of systems that exhibit discontinuity are introduced with the Kurzweil equations associated with this class of equations. The formulations are simple extensions of the methods applied by Schwabik [10] to ODEs to this present noncommutative quantum setting. Here the solutions of a QSDE are discontinuous functions of bounded variation that is they have the same properties as the Kurzweil equations associated with QSDEs introduced in [1]

Maximal Solution Non Classical Differential Equation Association with Kurzweil Equations

We prove some new results on existence of solutions to first-order non classical ordinary differential equations associated with Kurzweil equations. Our existence results lean on new definitions of lower and upper solutions introduced in this article. The existence of a maximal solution is guaranteed when the local uniqueness property in the future is established. These results could be of great value in applications to the theory of non classical differential equations in locally convex spaces

Gravitational waves from quasi-spherical black holes

A quasi-spherical approximation scheme, intended to apply to coalescing black holes, allows the waveforms of gravitational radiation to be computed by integrating ordinary differential equations.Comment: 4 revtex pages, 2 eps figure

Buoyancy and thermal radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition

This study is devoted to investigate the Buoyancy and thermal radiation effects on the laminar boundary layer about a flat-plate in a uniform stream of fluid (Blasius flow), and about a moving plate in a quiescent ambient fluid (Sakiadis flow) both under a convective surface boundary condition. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by using shooting technique along side with the sixth order of Runge-Kutta integration scheme and the variations of dimensionless surface temperature and fluid-solid interface characteristics for different values of Prandtl number Pr, radiation parameter NR, parameter a and the local Grashof number Grx, which characterizes our convection processes are graphed and tabulated. Quite different and interesting behaviours were encountered for Blasius flow compared with a Sakiadis flow. A comparison with previously published results on special cases of the problem shows excellent agreement

Two Steps Block Method for the Solution of General Second Order Initial Value Problems of Ordinary Differential Equation

In this paper, an implicit block linear multistep method for the solution of ordinary differential equation was extended to the general form of differential equation. This method is self starting and does not need a predictor to solve for the unknown in the corrector. The method can also be extended to boundary value problems without additional cost. The method was found to be efficient after being tested with numerical problems of second order

On Existence of Solution for Impulsive Perturbed Quantum Stochastic Differential Equations and the Associated Kurzweil Equations

Existence of solution of impulsive Lipschitzian quantum stochastic differential equations (QSDEs) associated with the Kurzweil equations are introduced and studied. This is accomplished within the framework of the Hudson-Parthasarathy formulation of quantum stochastic calculus and the associated Kurzweil equations. Here again, the solutions of a QSDE are functions of bounded variation, that is they have the same properties as the Kurzweil equations associated with QSDEs introduced in [1, 4]. This generalizes similar results for classical initial value problems to the noncommutative quantum setting

Converse Variational Stability for Kurzweil Equations Associated with Quantum Stochastic Differential Equations

In analogous to classical ordinary differential equations, we study and establish results on converse variational stability of solution of quantum stochastic differential equations (QSDEs) associated with the Kurzweil equations. The results here generalize analogous results for classical initial value problems. The converse variational stability guaranteed the existence of a Lyapunov function when the solution is variationally stabl

Effects of chemical reaction, thermal radiation, internal heat generation, Soret and Dufour on chemically reacting MHD boundary layer flow of heat and mass transfer past a moving vertical plate with suction/injection

In the present analysis, we study the two-dimensional, steady, incompressible electrically conducting, laminar free convection boundary layer flow of a continuously moving vertical porous plate in a chemically reactive medium in the presence of transverse magnetic field, thermal radiation, chemical reaction, internal heat generation and Dufour and Soret effect with suction/injection. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The problem is solved numerically using shooting techniques with the sixth order Runge-Kutta integration scheme. Comparison between the existing literature and the present study were carried out and found to be in excellent agreement. The influence of the various interesting parameters on the flow and heat transfer is analyzed and discussed through graphs in detail. The values of the local Nusselt number, Skin-friction and the Sherwood number for different physical parameters are also tabulated. Comparison of the present results with known numerical results is shown and a good agreement is observed

Effects of Ohmic Heating,Radiation and Viscous Dissipation on Steady MHD Flow Near a Stagnation Point on an Isothermal Stretching Sheet in the Presence of Heat Generation

Aim of the paper is to examine the influences of radiation, heat generation, Ohmic heating and viscous dissipation on steady flow of a viscous incompressible electrically conducting fluid in the presence of uniform transverse magnetic field and variable free stream near a stagnation point on a stretching non-conducting isolhennal sheet. The governing equations of continuity, momentum, and energy are transformed into ordinary differential equations and solved numerically by shooting method alongside with Runge-Kutta sixth order. The velocity and temperature profiles are extensively discussed numerically and presented with the aid of graphs. Skin-friction coefficient and the Nusselt number at the sheet are derived, discussed and their numerical values for various values of physical parameters are COf11lared with the existing literature in tabular form and there are perfect agreements