VPM (continuation method or homotopy method) may be considered as special development and modification of classical Newton’s method, see [1] [5], [16]. The main idea of VPM admits short formulation: reducing of a given problem to some IVP for ODE. This fundamental principle of mathematical physics is well known, widely used and effective because IVP for ODE may be considered as a routine comput...

A laminar, two dimensional, steady boundary layer Newtonian conducting fluid flow passes over a permeable shrinking sheet in the presence of a uniform magnetic field is investigated. The governing equations have converted to ordinary nonlinear differential equations (ODE) by using appropriate similarity transformations. The main idea is to transform ODE with infinite boundary condition into oth...

This paper investigates guaranteed methods for estimating feasible parameter sets when the system under study is modelled with ordinary differential equations (ODE). The issue is to find the set of parameters such that the solution of the ODE remains within specified intervals at known time-data points. These intervals correspond usually to measurement uncertainty. This is a set inversion probl...

Ordinary differential equations (ODEs) are widely used in ecology to describe the dynamical behavior of systems of interacting populations. However, systems of ODEs rarely provide quantitative solutions that are close to real field observations or experimental data because natural systems are subject to environmental and demographic noise and ecologists are often uncertain about the correct par...

The paper is concerned with the finite-time stabilization of a coupled PDE–ODE system describing motion an overhead crane flexible cable. dynamics cable described by wave equation variable coefficient which affine function curvilinear abscissa along Using several changes variables, backstepping transformation, and stable second-order ODE for conveniently chosen variable, we prove that global oc...

In this work we analyse a PDE-ODE problem modelling the evolution of Glioblastoma, which includes an anisotropic nonlinear diffusion term with velocity increasing respect to vasculature. First, prove existence global in time weak-strong solutions using regularization technique via artificial ODE-system and fixed point argument. addition, stability results critical points are given under some co...

This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least squares (NLS) estimator is investigated in this study. A numerical algorithm such as the Runge-Kutta method is used to approximate the ODE solution. The asymptotic...

In this paper, the fault detection problem for nonlinear dynamic power systems based an observer is treated. The nonlinear dynamic model based on differential algebraic equations (DAE) is transformed in to ordinary differential equations (ODE). Three nonlinear observers are used and compared for generating the residual signals. Which are: the extended Kalman filter, the extended Kalman estimato...

In this paper, we prove the local controllability to positive constant trajectories of a nonlinear system two coupled ODE equations, posed in one-dimensional spatial setting, with nonlocal nonlinearities, and using only one localized control moving support. The model deal is derived from well-known reaction–diffusion Gray–Scott when diffusion coefficient first chemical species \(d_u\) tends 0 s...

to start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ode. then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. it is required to state that the infinite series method is a well-organized method for obtaining exact s...