The specific force equation has many applications in open channel flow problems. Quantifying of the hydraulic jump phenomenon is an important application of this equation. This equation has a direct solution only for the rectangular channels. The trial and error procedure as well as the graphical solution are the existing methods of solving hydraulic jump equations. No direct solutions are avai...

In this thesis, quantum-mechanical calculations within density-functional theory on metallic systems are presented. The overarching goal has been to investigate effects of disorder. In particular, one of the properties investigated is the bindingenergy shifts for core electrons in binary alloys using different theoretical methods. These methods are compared with each other and with experimental...

In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k + kh + h) for the solution of quasi-linear parabolic equation   , , , , xx x t u f x t u u u  , 0< x <1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline app...

Shape modeling using planar cubic algebraic curves calls for computing the real inflection points of these curves since inflection points represents important shape feature. A real inflection point is also required for transforming projectively a planar cubic algebraic curve to the normal form, in order to facilitate further analysis of the curve. However, the naive method for computing the inf...

Fourth-order Schrödinger equations have been introduced by Karpman and Shagalov to take into account the role of small fourth-order dispersion terms in the propagation of intense laser beams in a bulk medium with Kerr nonlinearity. In this paper we investigate the cubic defocusing fourth order Schrödinger equation i∂tu +∆ 2 u + |u|u = 0 in arbitrary space dimension R for arbitrary initial data....

Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Diff...

We construct thermodynamic potentials for two superionic phases of water [with body-centered cubic (bcc) and face-centered cubic (fcc) oxygen lattice] using a combination of density functional theory (DFT) and molecular dynamics simulations (MD). For this purpose, a generic expression for the free energy of warm dense matter is developed and parametrized with equation of state data from the DFT...