Stability tests for second order linear and nonlinear delayed models

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

Second Order Linear and Nonlinear Differential Equations'

Semismooth Methods for Linear and Nonlinear Second-order Cone Programs

The optimality conditions of a nonlinear second-order cone program can be reformulated as a nonsmooth system of equations using a projection mapping. This allows the application of nonsmooth Newton methods for the solution of the nonlinear second-order cone program. Conditions for the local quadratic convergence of these nonsmooth Newton methods are investigated. Related conditions are also giv...

Stability Analysis for Nonlinear Second Order Differential Equations with Impulses∗

In this paper we investigate the impulsive equation { (r(t)x′) + a(t)x + f (t, x, x′) = p(t), t ≥ t0, t 6= tk, x(tk) = ckx(tk − 0), x(tk) = dkx(tk − 0), k = 1, 2, 3, . . . , and establish a couple of criteria to guarantee the equations of this type to possess the stability, including boundedness and asymptotic properties. Some examples are given to illustrate our results and the last one shows ...

Which Methodology is Better for Combining Linear and Nonlinear Models for Time Series Forecasting?

Both theoretical and empirical findings have suggested that combining different models can be an effective way to improve the predictive performance of each individual model. It is especially occurred when the models in the ensemble are quite different. Hybrid techniques that decompose a time series into its linear and nonlinear components are one of the most important kinds of the hybrid model...