A typical two-dimensional airfoil with freeplay nonlinearity in pitch undergoing subsonic flow is studied via numerical integrationmethods.Due to the existence of the discontinuous nonlinearity, the classical fourth-order Runge-Kutta (RK4) method cannot capture the aeroelastic response accurately. Particularly, it is because the RK4 method is incapable of detecting the discontinuous points of t...

When solving certain evolution type PDE such as the Schrödinger equation, the Interaction Picture method is a valuable alternative to Split-Step methods. The Interaction Picture method has good computational features when used together with the standard 4th order Runge-Kutta scheme (giving rise to the RK4-IP method). In this paper we present an embedded Runge-Kutta scheme with orders 3 and 4wit...

When simulating trajectories by integrating time-continuous car-following models, standard integration schemes such as the forth-order Runge-Kutta method (RK4) are rarely used while the simple Euler’s method is popular among researchers. We compare four explicit methods: Euler’s method, ballistic update, Heun’s method (trapezoidal rule), and the standard forth-order RK4. As performance metrics,...

This paper addresses the dynamic behaviour of a chemical oscillator arising from the series coupling of two Brusselators. Of particular interest is the study of the associated Hopf bifurcation and double-Hopf bifurcations. The motion of the oscillator may either be periodic (bifurcating from a Hopf-type critical point), or quasi-periodic (bifurcating from a compound critical point). Furthermore...

A new method for approximate analytic series solution called multistep Laplace Adomian Decomposition Method MLADM has been proposed for solving the model for HIV infection of CD4 T cells. The proposed method is modification of the classical Laplace Adomian Decomposition Method LADM with multistep approach. Fourth-order Runge-Kutta method RK4 is used to evaluate the effectiveness of the proposed...

In this paper, we introduce a modification of the Picard iteration method (PIM) using Padé approximation and so called Picard-Padé technique. Special attention is given to study the convergence analysis of the proposed method. Convergence analysis is reliable enough to estimate the maximum absolute error of the solution given by PIM. A basic enzyme kinetics is used to test the effectiveness of ...

In this paper, a vaccination susceptible exposed infected recovered (VSEIR) model f o r tuberculosis in North Sumatera is discussed. The VSEIR model is formed by a system of nonlinear differential equations. The approximate solution of this model is obtained by using the step variational iteration method (SVIM) and variational iteration method (VIM). VIM used the general Lagrange multiplier in ...

The underwater glider has the advantages of low power, long endurance and high accuracy. Micro-Electro-MechanicalSystem (MEMS) grade inertial sensors are more suitable for an underwater glider because of their low cost and small size. Models of MEMS sensor noises which include not only the white noises and random walk terms but also the bias instabilities of the sensor noises are analyzed. The ...

In the present investigation, some novel analytical approximations to both unforced and forced pendulum–cart system oscillators are obtained. our two accurate effective approaches, namely, ansatz method with equilibrium point Krylov–Bogoliubov–Mitropolsky (KBM) method, implemented for analyzing problems.The obtained results compared Runge–Kutta (RK4) numerical approximation. The using KBM metho...

The goals of this study were to develop a simplified finite element knee model, cosimulate this model with the motion of knee flexion/extension to demonstrate the concept of cosimulation, and choose an integrator to maximize the efficiency of the cosimulation process. A simplified model of the knee was used to simulate flexion/extension in FEBio. The femur was modeled as a fixed, rigid body, th...