The piecewise variational iteration method (VIM) for solving Riccati differential equations (RDEs) provides a solution as a sequence of iterates. Therefore, its application to RDEs leads to the calculation of terms that are not needed and more time is consumed in repeated calculations for series solutions. In order to overcome these shortcomings, we propose an easy-to-use piecewise-truncated VI...

In this investigation, two different models for coupled asymmetrical oscillators, known as, forced damped Duffing oscillators (FDDOs) are reported. The first model of FDDOs consists a nonlinear oscillator (FDDO) with linear oscillator, while the second is composed FDDOs. Krylov–Bogoliubov–Mitropolsky (KBM) method, carried out analyzing any model. To do that, reduced to decoupled system individu...

This thesis is concerned with an investigation of the control of responses of plate structures with piezoelectric layers and under complicated excitations modeled as a non-stationary random process. The plate structures and piezoelectric layers are both discretized by the mixed formulation finite element method (FEM). The investigation consists of three parts. The first part is a literature sur...

The damped parametric driven nonlinear pendulum equation/oscillator (NPE), also known as the disturbed NPE, is examined, along with some associated oscillators for arbitrary angles vertical pivot. For analyzing and solving current equation, we reduce this equation to Duffing (DDE) variable coefficients. After that, DDE coefficients divided into two cases. In first case, analytical approximation...

this paper presents approximate analytical solutions for nonlinear oscillators using the multi-step homotopy analysis method (msham). the proposed scheme is only a simple modification of the homotopy analysis method, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. several illustrat...

The aim of this article is to model and analyze an unsteady axisymmetric flow of non-conducting, Newtonian fluid squeezed between two circular plates passing through porous medium channel with slip boundary condition. A single fourth order nonlinear ordinary differential equation is obtained using similarity transformation. The resulting boundary value problem is solved using Homotopy Perturbat...

Analytical solution for hyperchaotic systems have attracted increasing interest in recent years. In this paper, numerical-analytical solution for hyperchaotic Rössler system is obtained via multistage homotopy analysis method (MSHAM). An analytical form of the solution within each time interval is given, which is not possible using standard numerical methods. The numerical results obtained by t...

Abstract: In engineering, physics, biomedical sciences and many other fields the regression function is known to satisfy a system of ordinary differential equations (ODEs). Our interest lies in the unknown parameters involved in the ODEs. When the analytical solution of the ODEs is not available, one approach is to use numerical methods to solve the system. A four stage Runge-Kutta (RK4) method...