In order to expand a formal linearization method on designing an observer for nonlinear dynamic and measurement systems, we exploit the discrete Fourier expansion that can reduce computational complexity. A nonlinear multidimensional dynamic system is considered by a nonlinear ordinary differential equation, and a measurement equation is done by a nonlinear equation. Defining a linearization fu...

Complete nonlinear differential-algebraic equation (DAE) sub-system models are considered in the paper when designing controllers of components in power systems. First-principle models are nonlinear DAE sub-system models, but they use non-local measurable variables to describe the mutual relation (interconnection) between component and the AC grid, and thus they are not suitable for designing d...

In this paper, the ( / ) G G  -expansion method is extended to solve fractional differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into ordinary differential equations of integer order. For illustrating the validity of this method, we apply it to fi...

We formulate a multi-scale perturbation technique to asymptotically solve weakly nonlinear hyperbolic equations. The method is based on a set of scaled characteristic coordinates. We show that this technique leads to a simplified system of ordinary differential equations describing the weakly nonlinear interaction between left and right running waves. Using this method, a uniformly valid first ...

In this article, the flow problem in a thin liquid film of second grade fluid over an unsteady stretching surface is investigated. By means of suitable transformations, the governing nonlinear partial differential equation has been reduced to the nonlinear ordinary differential equation. The developed nonlinear equation is solved analytically by using the homotopy analysis method (HAM). An expr...

He’s variational iteration method [1, 2], which is a modified general Lagrange multiplier method [3], has been shown to solve effectively, easily and accurately a large class of nonlinear problems with approximations which converge quickly to accurate solutions. It was successfully applied to autonomous ordinary differential equations [4], nonlinear partial differential equations with variable ...

in this paper, we use parametric form of fuzzy number, then aniterative approach for obtaining approximate solution for a classof nonlinear fuzzy fredholmintegro-differential equation of the second kindis proposed. this paper presents a method based on newton-cotesmethods with positive coefficient. then we obtain approximatesolution of the nonlinear fuzzy integro-differential equations by an it...

By using solutions of an ordinary differential equation, an auxiliary equation method is described to seek exact solutions of nonlinear evolution equations with variable coefficients. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients. As a result, new explicit solutions including solitary wave solutions and trigonometric function solutions...