The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. This method gives an analytic solution when ...

PURPOSE To assess how 4D flow MRI-based pressure and energy loss estimates correspond to net transstenotic pressure gradients (TPGnet) and their dependence on spatial resolution. METHODS Numerical velocity data of stenotic flow were obtained from computational fluid dynamics (CFD) simulations in geometries with varying stenosis degrees, poststenotic diameters and flow rates. MRI measurements ...

in this paper, the picard method is proposed to solve the bernoulli equation with fuzzy initial condition under generalized h-differentiability. the existence and uniqueness of the solution and convergence of the proposed method are proved in details. finally an example shows the accuracy of this method.

the current paper contributes a novel framework for solving a class of linear matrix differential equations. to do so, the operational matrix of the derivative based on the shifted bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. an error estimation of presented method is provided. numerical experiments are...

An 1D tight-binding version of the Dirac equation is considered; after checking that it recovers the usual discrete Schrödinger equation in the nonrelativistic limit, it is found that for two-valued Bernoulli potentials the zero mass case presents absence of dynamical localization for specific values of the energy, albeit it has no continuous spectrum. For the other energy values (again excludi...

Abstract: In this paper, new algorithms called the “Modified exp( ́Ω)-expansion function method” and “Improved Bernoulli sub-equation function method” have been proposed. The first algorithm is based on the exp( ́Ω(ξ))-expansion method; the latter is based on the Bernoulli sub-Ordinary Differential Equation method. The methods proposed have been expressed comprehensively in this manuscript. The a...

In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized to transform the differential equation to a matrix equation which corresponds to a system of algebraic equations with unknown Bernoulli coefficients. This met...

A special attention is paid to the motion of flexible links in a robotic configuration. The elastic deformation is a dynamic value which depends on the total dynamics of the robot system movements. The Euler-Bernoulli equation should be expanded according to the requirements of the motion complexity of elastic robotic systems. The EulerBernoulli equation (based on the existing laws of dynamics)...

Since the 1940s there has been an interest in the question of why social networks often give rise to two antagonistic factions. Recently a dynamical model of how and why such a balance might occur was developed. This note provides an introduction to the notion of social balance and a new (and simplified) analysis of that model. This new analysis allows us to choose general initial conditions, a...