in this article, vibration analysis of an euler-bernoulli beam resting on a pasternak-type foundation is studied. the governing equation is solved by using a spectral finite element model (sfem). the solution involves calculating wave and time responses of the beam. the fast fourier transform function is used for temporal discretization of the governing partial differential equation into a set ...

This survey paper reports on the properties of the fourth-order Bessel-type linear ordinary differential equation, on the generated self-adjoint differential operators in two associated Hilbert function spaces, and on the generalisation of the classical Hankel integral transform. These results are based upon the properties of the classical Bessel and Laguerre second-order differential equations...

This article looks at the steady flow of Micropolar fluid over a stretching surface with heat transfer in the presence of Newtonian heating. The relevant partial differential equations have been reduced to ordinary differential equations. The reduced ordinary differential equation system has been numerically solved by Runge-Kutta-Fehlberg fourth-fifth order method. Influence of different involv...

We consider a nonlinear partial differential equation for complexvalued functions which is related to the two-dimensional stationary Schrödinger equation and enjoys many properties similar to those of the ordinary differential Riccati equation as, e.g., the famous Euler theorems, the Picard theorem and others. Besides these generalizations of the classical “one-dimensional” results we discuss n...

A completely integrable partial differential equation is one which has a Lax representation, or, more precisely, can be solved via a linear integral equation of Gel'fand-Levitan type, the classic example being the Korteweg-de Vries equation. An ordinary differential equation is of Painlev type if the only singularities of its solutions in the complex plane are poles. It is shown that, under cer...

Sunto. – In this note we survey some recent results on the well-posedness of the ordinary differential equation with non-Lipschitz vector fields. We introduce the notion of regular Lagrangian flow, which is the right concept of solution in this framework. We present two different approaches to the theory of regular Lagrangian flows. The first one is quite general and is based on the connection ...

GOAL: The NTW package allows the computation of the interaction network of n genes (A, nxn) based on m independent experiments collecting gene expression profiles (X, nxm) with or without the associated transcriptional pertubation matrix (P, nxm, contains the direct targets of each of the m perturbation done on the system). The approach is based on ordinary differential equations (ODE) and 3 op...

A conceptually new approximation method to study the time-frequency properties of dynamical systems characterized by linear ordinary differential equations is presented. We bypass solving the differential equation governing the motion by writing the exactWigner distribution corresponding to the solution of the differential equation. The resulting equation is a partial differential equation in t...

Nowadays, fractional calculus are used to model various different phenomena in nature, but due to the non-local property of the fractional derivative, it still remains a lot of improvements in the present numerical approaches. In this paper, some new numerical approaches based on piecewise interpolation for fractional calculus, and some new improved approaches based on the Simpson method for th...

Efron, Hastie, Johnstone and Tibshirani (2004) proposed Least Angle Regression (LAR), a solution path algorithm for the least squares regression. They pointed out that a slight modification of the LAR gives the LASSO (Tibshirani, 1996) solution path. However it is largely unknown how to extend this solution path algorithm to models beyond the least squares regression. In this work, we propose a...