By now it is clear that computational science is one of the bases, together with theory and experiments, of scientific inquiry. A carefully crafted computational model/experiment can replace a very expensive or unrealizable experimental setting, and it can give new insight into the theoretical developments of a specific discipline. Discussions about computer aided simulation and high performanc...

The PDE system introduced in Maity et al. (2019) describes the interaction of surface water waves with a floating solid, and takes into account viscosity µ fluid. In this work, we study Cummins type integro-differential equation for unbounded domains, that arises when is linearized around equilibrium conditions. A proof input-output stability given, thanks to diffusive representation generalize...

The aim of this study was to determine whether dobutamine, dopamine, or milrinone (a phosphodiesterase [PDE] III inhibitor) would support cardiac function that had been attenuated by administration of the beta-blocker, carvedilol (0.2, 0.4, or 0.8 mg/kg). Hemodynamic and cardiac parameters including the heart rate (HR), left-ventricular fractional shortening (FS), and arterial pressure were mea...

We suggest generalizations of the mathematical model of magnetic insulation, described by multidimensional quasi potential ODE system or PDE system with two-dimensional Laplace operator. Existence conditions of the first integrals of a certain type for the class of nonlinear quasi potential systems, including the model vacuum diode are obtained. Integrability of the vacuum diode models is justi...

Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systema...

In this paper, we study a new class of equations called mean-field backward stochastic differential (BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H > 1/2. First, the existence and uniqueness BSDEs are obtained. Second, comparison theorem solutions is established. Third, as an application, connect nonlocal partial equation (PDE, short), derive relationship between ...

In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...