Stability and persistence in ODE modelsfor populations with many stages by Guihong Fan, Yijun Lou, Horst R. Thieme, Jianhong Wu

“…A model of ordinary differential equations is formulated for populationswhich are structured by many stages. …”
Get full text

Detection of the onset of numerical chaotic instabilities by lyapunov exponents by Alicia Serfaty De Markus

“…It is commonly found in the fixed-step numerical integration of nonlinear differential equations that the size of the integration step is opposite related to the numerical stability of the scheme and to the speed of computation. …”
Get full text

Prediction of influenza peaks in Russian cities: Comparing the accuracy of two SEIR models by Vasiliy N. Leonenko, Sergey V. Ivanov

“…The first one is a continuous SEIR model described by a system of ordinary differential equations. The second one is a discrete model formulated as a set of difference equations, which was used in the Baroyan-Rvachev modeling framework for the influenza outbreak prediction in the Soviet Union. …”
Get full text

Stochastic Predator-Prey System Subject to Lévy Jumps by Xinzhu Meng, Xiaohong Wang

“…In addition, we obtain the sufficient conditions for almost sure permanence in mean and stochastic permanence of the system by using the theory of impulsive stochastic differential equations. Finally, we discuss the biological implications of the main results and show that the large noise can make the system go extinct. …”
Get full text

Soret and Dufour Effects on Natural Convection Flow Past a Vertical Surface in a Porous Medium with Variable Viscosity by M. B. K. Moorthy, K. Senthilvadivu

“…The governing equations of continuity, momentum, energy, and concentrations are transformed into nonlinear ordinary differential equations, using similarity transformations, and then solved by using Runge-Kutta-Gill method along with shooting technique. …”
Get full text

Parametric and self-excited oscillations under nonlinear parametric action and lag in elasticity by Alifov Alishir

“…To solve the differential equations of the system motion, the direct linearization method was used and equations for non-stationary and stationary modes of oscillations were derived. …”
Get full text

Topology in nonlinear extensions of hypernumbers by M. S. Burgin

“…Modern theory of dynamical systems is mostly based on nonlinear differential equations and operations. At the same time, the theory of hypernumbers and extrafunctions, a novel approach in functional analysis, has been limited to linear systems. …”
Get full text

Analysis on Cage Dynamic Characteristic of Ultra-low Temperature Angular Contact Ball Bearing by Jing Liu, Yanguang Ni, Wenhu Zhang, Sier Deng

“…Based on the dynamics theory of the rolling bearings， the dynamics differential equations of angular contact ball bearing are established in which the pocket shape of the cage is elliptical. …”
Get full text

Modeling Multicellular Systems Using Subcellular Elements by T. J. Newman

“…We present here a detailed description of the model, and use successive mean-field approximations to connect it to more coarse-grained approaches, such as discrete cell-based algorithms and coupled partial differential equations. We also discuss efficient algorithms for encoding the model, and give an example of a simulation of an epithelial sheet. …”
Get full text

Study on Vibration Characteristic of Trilobe Raceway Cylindrical Roller Bearing with Elastic Support by Sun Xue, Deng Sier, Zhang Yuanjun, Chen Guoding

“…Based on dynamics analysis of rolling bearing,the dynamics differential equations for cylindrical roller bearing with trilobe raceway and elastic support are established. …”
Get full text

Numerical Solutions of Odd Order Linear and Nonlinear Initial Value Problems Using a Shifted Jacobi Spectral Approximations by A. H. Bhrawy, M. A. Alghamdi

“…A shifted Jacobi Galerkin method is introduced to get a direct solution technique for solving the third- and fifth-order differential equations with constant coefficients subject to initial conditions. …”
Get full text

On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications by Teng-fei Li, Heng-you Lan

“…In order to solve (partial) differential equations, implicit midpoint rules are often employed as a powerful numerical method. …”
Get full text

Reducing the Possibility of Ruin by Maximizing the Survival Function for the Insurance Company’s Portfolio by Masoud Komunte, Christian Kasumo, Verdiana Grace Masanja

“…The Hamilton–Jacobi–Bellman equation and integro-differential equation of Volterra type were obtained. The Volterra integro-differential equation for the survival function of the insurance company was converted to a third-order ordinary differential equation which was later converted into a system of first-order ordinary differential equations. …”
Get full text

Dynamic Effective Properties of Lead-Reinforced Epoxy Resin Composites with Differential Method by Haitao Zhu, Yongping Wan

“…The corresponding differential equations are numerically solved by the fourth-order Runge–Kutta method, and the dynamic effective modulus and density are obtained. …”
Get full text

Usage of computer algebra in teaching process by Aleksas Domarkas, Gintautas Misevičius, Violeta Pakalnytė, Albertas Pincevičius, Rimantas-Jonas Rakauskas

“…Namely, it is the problems of linear algebra, analyse of graphs, numerical calculation, integration, solution of differential equations, statistics for management, linear programming. …”
Get full text

Grey Prediction for Accuracy Life of Roller Pushing Mechanism by Zhang Liping

“…The albino form of differential equations of grey system GM（ 1,1） is established. …”
Get full text

Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model – Supports Movement Excitation by Jan Freundlich

“…This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. …”
Get full text

The Analytical Form of the Dispersion Equation of Elastic Waves in Periodically Inhomogeneous Medium of Different Classes of Crystals by Nurlybek A. Ispulov, Abdul Qadir, Marat K. Zhukenov, Talgat S. Dossanov, Tanat G. Kissikov

“…In this paper by using analytical matrizant method set of equation of motions in elastic media are reduced to equivalent set of first-order differential equations. Moreover, for given set of equations, the structure of fundamental solutions for the general case has been derived and also dispersion relations are obtained.…”
Get full text

Some new existence results of positive solutions for anisotropic variable exponent operator by Rafik Guefaifia, Salah Boulaaras, Rashid Jan

“…By deriving new existence results, the study advances the understanding of nonlinear partial differential equations in anisotropic and variable exponent settings. …”
Get full text

Three-dimensional guidance control for vehicle convoy and interception by Yihua Dong, Yuefen Tan, Jingang Zhao, Wencheng Wang

“…Based on the differential equations for the range, the pitch angle and the yaw angle between successive vehicles, the deviated pursuit and the proportional navigation are proposed to derive decentralized control strategy for vehicle convoy and interception control. …”
Get full text