In this paper, a heuristic scheme is used to obtain the numerical solution of the non linear ordinary differential equations (NLODEs). The approximate solutions of the given NLODEs are deduced as a linear combination of some log sigmoid basis functions with unknown parameters. The given NLODEs are converted into equivalent global error minimization problems. Genetic algorithm (GA) and a hybrid ...

The current paper focuses on some analytical techniques to solve the non-linear Duffing oscillator with large nonlinearity. Four different methods have been applied for solution of the equation of motion; the variational iteration method, He’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. The results reveal that approxim...

This paper demonstrates an equivalence between rotating magnetized shear flows and a stressed elastic beam. This results from finding the same form of dynamical equations after an asymptotic reduction of the axis-symmetric magnetorotational instability (MRI) under the assumption of almost-critical driving. The analysis considers the MRI dynamics in a non-dissipative near-equilibrium regime. Bot...

A method for the development of mathematical models for dynamic systems with arbitrary nonlinearides from measured data is described. The method involves the use of neural networks as embedded processors indynamic system simuation models. The technique is demonstrated through generation of models for anharmonic oscillators described by the Duffing Equation and the Van der Pol Equation from meas...

A modified variational approach called Global Error Minimization (GEM) method is developed for obtaining an approximate closed-form analytical solution for nonlinear oscillator differential equations. The proposed method converts the nonlinear differential equation to an equivalentminimization problem. A trial solution is selectedwith unknown parameters. Next, the GEM method is used to solve th...