We study differentiability properties in a particular case of the Palmer’s linearization Theorem, which states the existence of an homeomorphism H between the solutions of a linear ODE system having exponential dichotomy and a quasilinear system. Indeed, if the linear system is uniformly asymptotically stable, sufficient conditions ensuring that H is a C preserving orientation diffeomorphism ar...

In this study, accurate analytical solution for the nonlinear free vibration of an oscillator with inertia and static type cubic nonlinearities is derived. This solution is called He’s Variational Iteration Method (VIM). Comparing this method with numerical integration solutions using a built-in ODE-solver in MATLAB and He’s Homotopy Analysis Method (HAM) is shown its drastic approximation. By ...

In this paper we consider a nonlinear system of differential equations arising in tumour invasion which has been proposed in [1]. The system consists of two PDEs describing the evolution of tumour cells and proteases and an ODE which models the concentration of the extracellular matrix. We prove local existence and uniqueness of solutions in the class of Hölder spaces. The proof of local existe...

The phenomenon of convective flow with heat and mass transfer has been studied extensively due to its applications in various fields. effects nonlinear thermal radiation (NLTR), slip, thermal-diffusion (Soret) diffusion-thermo (Dufour) on magenoto-hydrodynamic (MHD) towards a stretching cylinder the presence triple stratification (TSF) are investigated this paper. governing equations transforme...

The temperature distribution in a conductive-radiative rectangular profiled annular fin with internal heat generation is scrutinized the present investigation. nonlinear variation of thermal conductivity and transfer coefficient governed by power law considered. analytical approximation for non-dimensional profile obtained using differential transform method (DTM)-Pade approximant. nondimension...

For a second order nonlinear ordinary differential equation (ODE), a singular boundary value problem (BVP) is investigated which arises in hydromechanics and nonlinear field theory when static centrally symmetric bubble type (droplet type) solutions are sought. Being defined on a semi infinite interval 0 < r <∞, this ODE, with a polynomial nonlinearity of the third order with respect to a desir...

In this paper we study the properties of an age-structured MSEIR epidemic model. Existence, uniqueness and positivity of the strict solution of the problem are proved by using semigroup techniques. Moreover, the expression of the total population density by means of a suitable nonlinear semigroup is given. Finally, a semplified system of ODE is proposed and the equilibrium solutions with stabil...

We propose a model order reduction (MOR) approach for networks containing simple and complex components modeled by linear ODE and nonlinear PDE systems respectively. These systems are coupled through the network topology using the Kirchhoff laws. We consider as application MOR for electrical networks, where semiconductors form the complex components. POD combined with discrete empirical interpo...

We present a numerical scheme for an efficient discretization of nonlinear systems of differential equations subjected to highly oscillatory perturbations. This method is superior to standard ODE numerical solvers in the presence of high frequency forcing terms, and is based on asymptotic expansions of the solution in inverse powers of the oscillatory parameter ω, featuring modulated Fourier se...