We present the circuit-level verification of a common arbiter circuit. To perform this verification, we address three issues. First, we present a specification for the arbiter and show how this specification amounts to a set of topological constraints on trajectories of the continuous model. Second, we show that computing bounding sets for these trajectories is complicated by stiffness of the d...

In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...

In this work, the homotopy perturbation method is developed and formulated to find an approximate-analytical solution of fuzzy initial value problems involving a nonlinear first order ordinary differential equation. HPM allows for the solution of FIVPs to be calculated in the form of an infinite series in which the components can be easily computed. An efficient algorithm is proposed of HPM on ...

‎in this paper‎, ‎first we discuss a local stability analysis of model was introduced by p‎. ‎j‎. ‎mumby et‎. ‎al‎. ‎(2007)‎, ‎with $frac{gm^{2}}{m+t}$ as the functional response term‎. ‎we conclude that the grazing intensity is the important parameter to control the existence or extinction of the coral reef‎. ‎next‎, ‎we consider this model under the influence of the time delay as the bifurcat...

The focus of this paper is to clarify the concepts of solutions of linear equations in interval, probabilistic, and fuzzy sets setting for real world tasks. There is a fundamental difference between formal definitions of the solutions and physically meaningful concepts of solution in applied tasks, when equations have uncertain components. For instance, a formal definition of the solution in te...

Partial differential equations are known to be increasingly important in today’s research, and their solutions paramount for tackling numerous real-life applications. This article extended the analytical scheme of homotopy analysis method (HAM) develop an approximate solution Fuzzy Differential Equations (FPDEs). The used its powerful tools, auxiliary function convergence-control parameter, opt...

in this paper we have solved analytically the schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...

Recently, we proposed an algebraic difference scheme, with extended stability properties, for linear boundary value problems involving stiff differential equations of first order. Here, an efficient approximation scheme is presented for matrix square roots, which provides the stabilization of that scheme in case of stiffness. It combines the use of low-rank matrix approximations from projection...

When solving numerically the stiff second order ODE system obtained after semidiscretizing the wave-type partial differential equation (PDE) with the finite element method (FEM), and similarly to the HHTα method, which allows the numerical damping of the undesirable high frequency modes associated to FEM semidiscretization, we have constructed a modification of the 2-order BDF method (the BDF2 ...

Fuzzy finite element solution of uncertain neutron diffusion equation for imprecisely defined homogeneous triangular bare reactor S. Nayak and S. Chakraverty * Department of Mathematics, National Institute of Technology, Rourkela, Odisha -769008, India Abstract: Scattering of neutron collision inside a reactor depends upon geometry of the reactor, diffusion coefficient and absorption coefficien...