Process integration in Software Engineering Environments (SEE) is very important to allow tool integration. In this paper, we present a knowledge-based approach to improve process integration in ODE, an ontology-based SEE.

Complete nonlinear differential-algebraic equation (DAE) sub-system models are considered in the paper when designing controllers of components in power systems. First-principle models are nonlinear DAE sub-system models, but they use non-local measurable variables to describe the mutual relation (interconnection) between component and the AC grid, and thus they are not suitable for designing d...

In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G′/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expr...

This paper suggests a new approach to the problem of harmonic signal estimation. The idea is to model the harmonic signal as a function of the state of a second order nonlinear ordinary differential equation (ODE). The function of the right hand side of the nonlinear ODE is parameterized with a polynomial model. A Kalman filter and an extended Kalman filter are then developed. The proposed meth...

Purely numerical methods do not always provide an accurate way to find all the global solutions to nonlinear ODE on infinite intervals. For example, finite-difference methods fail to capture the asymptotic behavior of solutions, which might be critical for ensuring global existence. We first show, by way of a detailed example, how asymptotic information alone provides significant insight into t...

Which is the minimum order an autonomous nonlinear ordinary differential equation (ODE) needs to have to be able to model a periodic signal? This question is motivated by recent research on periodic signal analysis, where nonlinear ODEs are used as models. The results presented here show that an order of two of the ODE is sufficient for a large class of periodic signals. More precisely, conditi...

In this paper, the modified Korteweg-de Vries (mKdV) equation with variable coefficients (vc-mKdV equation) is investigated via two kinds of approaches and symbolic computation. On the one hand, we firstly reduce the vc-mKdV equation to a second-order nonlinear nonhomogeneous ODE using travelling wave-like similarity transformation. And then we obtain its many types of exact fractional solution...