We study the l1-error of a Hamiltonian-preserving scheme, developed in [11], for the Liouville equation with a piecewise constant potential in one space dimension. This problem has important applications in computations of the semiclassical limit of the linear Schrödinger equation through barriers, and of the high frequency waves through interfaces. We use the l1-error estimates established in ...

We study the l1-error of a Hamiltonian-preserving scheme, developed in [11], to the Liouville equation with a piecewise constant potential in one space dimension. This problem has important applications in computations of the semiclassical limit of the linear Schrödinger equation through barriers, and of the high frequency waves through interfaces. We use the l1-error estimates established in [...

The improved Boussinesq equation is studied in this paper. Control properties for this equation posed on a bounded interval are first considered. When the control acts through the Dirichlet boundary condition the linearized system is proved to be approximately but not spectrally controllable. In a second part, the equation is posed on the one-dimensional torus and distributed moving controls ar...

The question whether classical solutions of the surface quasi-geostrophic (SQG) equation can develop finite-time singularities remains open. This paper presents new numerical computations of the solutions to the SQG equation corresponding to several classes of initial data previously proposed by Constantin et al. (Nonlinearity 7:1495–1533, 1994). By parallelizing the serial pseudo-spectral code...

Most researches on fluid dynamics are mostly dedicated to obtain the solutions of Navier-Stokes equation which governs fluid flow with particular boundary conditions and approximations. We propose an alternative approach to deal with fluid dynamics using the lagrangian. We attempt to develop a gauge invariant lagrangian which reconstructs the Navier-Stokes equation through the Euler-Lagrange eq...

The famous Perona-Malik (P-M) equation which was at first introduced for image restoration has been solved via various numerical methods. In this paper we will solve it for the first time via applying a new numerical method called the Variational Iteration Method (VIM) and the correspondent approximated solutions will be obtained for the P-M equation with regards to relevant error analysis. Thr...

The famous Perona-Malik (P-M) equation which was at first introduced for image restoration has been solved via various numerical methods. In this paper we will solve it for the first time via applying a new numerical method called Homotopy Perturbation Method (HMP) and the correspondent approximated solutions will be obtained for the P-M equation with regard to relevant error analysis. Through ...

Aim: This study is aimed to assess the health and well-being benefits of gardening between gardeners non-gardeners. Methods: A total 400 respondents participated in which was equally sampled Criterion sampling utilized participant selection. The standardized questionnaires conducted Central Philippines. a quasi-experimental post-test only design. T-test independent samples analysis. Results: Re...

Today almost all ecosystems on Earth are directly or indirectly influenced by human activity. Most species occur in ecosystems that are managed by humans and only a small fraction of biodiversity exists in protected areas. Therefore, human dominated areas must also be considered for conservation of biodiversity. I have studied the effect of urbanization and green area management on bumble bees,...