We construct two variable-step linearly implicit Runge–Kutta methods of orders 3 and 4 for the numerical integration of the semidiscrete equations arising after the spatial discretization of advection–reaction–diffusion equations. We study the stability properties of these methods giving the appropriate extension of the concept of L-stability. Numerical results are reported when the methods pre...

A physically-plausible simulation of snow is a challenging task. The method we analyze in this thesis is a Material Point Method (MPM), that has been adjusted to accommodate both the fluid-like and the granular properties of snow. We analyze the simulation in four aspects. One, the noise generated from problems in numerical stability. Two, we analyze the domain in which simulation parameters pe...

In this paper, we study numerically the existence and stability of some special solutions of the nonlinear beam equation: utt +uxxxx +u− |u|p−1u = 0 when p = 3 and p = 5. First we show the existence and the orbital stability of the standing wave solutions: u(x, t) = eφω(x). Next, we study the existence and linear stability of the traveling wave solutions: u(x, t) = φ(x + ct). For both types of ...

We construct curve counting invariants for a Calabi-Yau threefold Y equipped with a dominant birational morphism π : Y → X. Our invariants generalize the stable pair invariants of Pandharipande and Thomas which occur for the case when π : Y → Y is the identity. Our main result is a PT/DT-type formula relating the partition function of our invariants to the Donaldson-Thomas partition function in...

We consider a fully discrete implicit nite element approximation of a model for phase separation of a multi-component alloy. We prove existence, uniqueness and stability of the numerical solution for a suuciently small time step. We prove convergence to the solution of the associated continuous problem. We perform a linear stability analysis of the equations and describe some numerical experime...

We study linear variable coeecient control problems in descriptor form. Based on a behaviour approach and the general theory for linear diierential algebraic systems we give the theoretical analysis and describe numerically stable methods to determine the structural properties of the system like solvability, regularity, model consistency and redundancy. We also discuss regularization via feedback.

We develop a theory of difference approximations to absorbing boundary conditions for the scalar wave equation in several space dimensions. This generalizes the work of the author described in [8]. The theory is based on a representation of analytical absorbing boundary conditions proven in [8]. These conditions are defined by compositions of first-order, one-dimensional differential operators....

Process studies focus attention on how itnd why things emerge, develop, grow, or terminate over time. We identify various ontological assumptions underl)ring process research, explore its methods and challenges, and draw out some of its substantive contributions revealed in this Special Research Forum on Process Studies of Change in Organization and Management. Process studies take time serious...

Many multi-branch companies transact from different branches. Each branch of such a company maintains a separate database over time. The variation of sales of an item over time is an important issue. Thus, we introduce the notion of stability of an item. Stable items are useful in making many strategic decisions for a company. Based on the degree of stability of an item, we design an algorithm ...

The lattice Boltzmann equations for the linear diffusion modeling in cases of D2Q5, D2Q7 and D2Q9 lattices are considered. Families of the numerical schemes with the dependence on scalar parameter are introduced. The stability analysis of schemes is performed in parameter space. The stability is studied numerically by von Neumann method. Optimal parameter values for the presented families are d...