The principal aim of this paper is to serve the numerical solution of an integralalgebraic 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 t...

In this paper, a new numerical method for solving the fractional Riccati differential  equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon  fractional-order Bernoulli functions approximations. First, the  fractional-order Bernoulli functions and  their properties are  presented. Then, an operational matrix of fractional order integration...

In this paper we give closed expressions for the deviation matrices of the M=M=1=1 and the M=M=1=N queue. It is applied to controlled queueing models by solving the dynamic programming optimality equation for Bernoulli policies, after which we can execute a single step of policy iteration, by calculating the bias vector of the Bernoulli policies directly from the deviation matrix.

In this paper, we use Hermite cubic finite elements to approximate the solutions of a nonlinear Euler– Bernoulli beam equation. The equation is derived from Hollomon’s generalized Hooke’s law for work hardening materials with the assumptions of the Euler–Bernoulli beam theory. The Ritz–Galerkin finite element procedure is used to form a finite dimensional nonlinear program problem, and a nonlin...

The flow of blood through the cardiovascular system depends on basic principles of liquid flow in tubes elucidated by Bernoulli and Poiseuille. The elementary equations are described involving pressures related to velocity, acceleration/deceleration, gravity, and viscous resistance to flow (Bernoulli-Poiseuille equation). The roles of vascular diameter and number of branches are emphasized. In ...

For linear partial differential equations, there exist well-developed classical methods of their analytical solution, which, in particular, includes the separation of variables, different integral transforms, Fourier series and their generalizations. At the same time, the study of symmetry properties of such equations is important, first of all, for the development of methods of symmetry analys...