First Riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. An analytical approximation of the solution of nonlinear differential Riccati equation is investigated using the Adomian decomposition method. An application in optimal control is presented. The solution in different order of approximations and different methods of approximat...

This paper addresses dynamic optimization of a large-scale natural gas processing plant through the formulation of rigorous unit dynamic models. The resulting differential-algebraic equation (DAE) optimization problem is solved with an advanced simultaneous strategy that transforms the original problem into a nonlinear program. Emphasis has been given to detailed thermodynamic and solubility ca...

In this paper, a nonlinear stiff differential equation is solved by using the Rosenbrock iterative method, modified homotpy analysis method and power series method. The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relations. Some numerical examples are studied to demonstrate the accuracy of the presented meth...

In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0

The homogeneous balance method can be used to construct exact traveling wave solutions of nonlinear partial differential equations. In this paper, this method is used to construct new soliton solutions of the (3+1) Jimbo--Miwa equation.

A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear differential equations have exact solutions which are general solution of the simplest integrable e...

In this paper, we implemented the Modified Iteration Perturbation Method (MIPM) for approximating the periodic behavior of a tapered beam. This problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. The solution is quickly convergent and does not need complicated calculations. Comparing the results of the MIPM with the exact solution shows that this...

friction is a nonlinear phenomenon which has destructive effects on performance of control systems. to obviate these effects, friction compensation is an effectual solution. in this paper, an adaptive technique is proposed in order to eliminate limit cycles as one of the undesired behaviors due to presence of friction in control systems which happen frequently. the proposed approach works for n...

We present a method to obtain approximate polynomial solutions for a class of second order nonlinear differential equations arising in heat transfer problems. We apply this method to find a approximate polynomial solution for the nonlinear temperature distribution equation of a thick rectangular fin. Key-Words: Nonlinear differential equation; boundary value problem; ε -approximate analytical a...