in this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the maclaurin series of the exact solution. nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. these equations equip a significant mathematical model for dynamical systems. the accuracy o...

In literature many chaotic systems, based on third-order jerk equations with different nonlinear functions, are available. A jerk system is taken to be a part of dynamical systems that can exhibit regular and chaotic behavior. By extension, a hyperjerk system can be described as a dynamical system with nth-order ordinary differential equations where n is 4 or up to. Hyperjerk systems have been ...

The DC analysis and transient analysis parts of the general electrical circuit analysis program ESACAP are parallelized to run on the Intel iPSC. Most of the program runs unchanged on the cube manager. Only the solution of the systems of nonlinear algebraic equations is parallelized to run on the hypercube parallel computer. The nonlinear equations arise either from the DC problem or from the d...

Annals of Probability 31(2003), 2109-2135. Invariant man-ifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for stochastic ordinary differential equations is relatively mature. In this paper, we present a unified theory of invarian...

Combining recent moment and sparse semidefinite programming (SDP) relaxation techniques, we propose an approach to find smooth approximations for solutions of nonlinear differential equations. Given a system of nonlinear differential equations, we apply a technique based on finite differences and sparse SDP relaxations for polynomial optimization problems (POP) to obtain a discrete approximatio...

The Mathematica implementation of the tanh and sech-methods for computing exact travelling wave solutions of nonlinear partial differential equations (PDEs) is presented. These methods also apply to ordinary differential equations (ODEs). New algorithms are given to compute polynomial solutions of ODEs and PDEs in terms of the Jacobi elliptic functions. An adaptation of the tanh-method to nonli...

The effects of chemical reaction, thermal stratification, Soret and Dufour numbers on magneto-hydrodynamic free convective heat and mass transfer of a viscous, incompressible,and electrically conducting fluid on a vertical stretching surface embedded in a saturated porous medium are presented. A similarity transform is used to reduce the governing partial differential equations into a syste...

Although the solutions with respect to time are commonly sought when analyzing the behavior of dynamic systems, there are other expressions that can be as revealing and important. Specifically, motion constants, which are time independent algebraic or transcendental equations involving the system states, can provide a broad view of a system’s motion. Locally, at least, the motion constants of a...

Algorithms are presented for the tanhand sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and PDEs in terms of Jacobi’s elliptic functions. For systems with parameters, the algorithms determine the conditions on the parameters so that the differential eq...

Sufficient conditions of interval absolute stability of nonlinear control systems described in terms of systems of the ordinary differential equations with delay argument and also neutral type are obtained. The Lyapunov-Krasovskii functional method in the form of the sum of a quadratic component and integrals from nonlinearity is used at construction of statements.