In this paper we develop numerical techniques of order 2, 4 and 6 for the solution of a fourth order linear equation. A priori error bound is obtained for the fourth order method to prove the convergence of the finite difference scheme. A sufficient condition guaranteeing the uniqueness of the solution of the boundary value problem is also given. Numerical illustrations are tabulated and result...

A priori bounds are derived for the discrete solution of second-order elliptic partial differential equations (PDEs). The bounds have two contributions. First, the influence of boundary conditions is taken into account through a discrete maximum principle. Second, the contribution of the source field is evaluated in a fashion similar to that used in the treatment of the continuous a priori oper...

A language L ⊆ A∗ is literally idempotent in case that uav ∈ L if and only if uav ∈ L for each u, v ∈ A∗, a ∈ A. Such classes result naturally by taking all literally idempotent languages in a classical (positive) variety or by considering a certain closure operator. We initiate their systematic study. Various classes of such languages can be characterized using syntactic methods. A starting ex...

This communication describes the results of bubble rise simulations using a lattice Boltzmann method and a front-tracking finite-difference method. The simulations, performed in a 2-D periodic box, consider two specific examples: a steadily rising bubble and a bubble rising in an oscillatory manner with accompanying shape change. We compare the shapes and rise velocities of the steadily rising ...

ACKNOWLEDGEMENTS I would like to truly thank all of my committee members for their encouragement and guidance in the preparation of this thesis. I especially want to express my gratitude to Dr. Kevin Clarno for his insight and assistance. My advisor, Dr. Cassiano de Oliveira, has been immensely helpful with his continuous encouragement and unique perspectives. Perhaps most of all, I want to tha...

Abstract. The interior of the Earth is heterogeneous with different material and may have complex geometry. The free surface can also be uneven. Therefore, the use of a meshless method with the possibility of using and irregular grid-point distribution can be interest for modelling this kind of problem. This paper shows the application of Generalized Finite Difference Method (GFDM) to the probl...

We present a domain decomposition technical for computing the quantum transport phenomena in complex nano-structures. In regular sub-domains, the subband decomposition method is applied, while the finite difference method is used on small irregular sub-domains where the subband decomposition is not applicable. This new approach preserves the efficiency of the original subband decomposition meth...

During the process of bubbles interacting with particles, the bubble movement velocity, jetting phenomenon, topological deformation, and even properties of flow field may demonstrate novel variation. To investigate these characteristics, the lattice Boltzmann method (LBM) which is based on kinetic theory is adopted to build up the three dimensional coupled model. The gas-liquid interface with l...

In this study, the finite difference method is applied to an optimal control problem controlled by two functions which are in the coefficients of two-dimensional Schrodinger equation. Convergence of the finite difference approximation according to the functional is proved. We have used the implicit method for solving the two-dimensional Schrodinger equation. Although the implicit scheme obtaine...

It has been previously shown that the temporal integration of hyperbolic partial differential equations may , because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic p.d.e's (linear and non-linear) whose boundary treatment is done via t...