Many dynamical systems described by nonlinear ODEs are unstable. Their associated solutions do not converge towards an equilibrium point, but rather some invariant subset of the state space called attractor set. For a given ODE, in general, existence, shape and structure sets ODE unknown. Fortunately, sublevel Lyapunov functions can provide bounds on ODEs. In this paper we propose new character...

We consider a coupled PDE–ODE model governing the bacterial dynamics of anaerobic biodegradation household waste in landfill. The biological activity, represented with non linear system ordinary differential equations (ODE), takes place an unsaturated porous medium by Darcy law. transform initial into fully PDE where distribution is spatialized as reaction–diffusion equations. carry out mathema...

We consider the problem of estimating a nonlinear state-space model whose state process is driven by an ordinary differential equation (ODE) or a stochastic differential equation (SDE), with discrete-time data. We propose a new estimation method by minimizing the conditional least squares (CLS) with the conditional mean function computed approximately via unscented Kalman filter (UKF). We deriv...

The solution of a nonlinear boundary value problem in ordinary differential equations the form $ L(x(t))+f(x(t)) = 0 can be obtained by solving associated system equations. In this paper, three-step iterative method with ninth order convergence is proposed to solve scheme kept free from second and higher Frechet derivatives make it computationally efficient. discretized produce which then solve...

Implicit/explicit (IMEX) Runge-Kutta (RK) schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS; such schemes implement an (often A-stable or better) implicit RK scheme for the stiff part of the ODE, which is often linear, and, simultaneously, a (more convenient) explicit RK scheme for the nonstiff part of the ODE, which is often nonlinear. Low-storag...

The structure of the blow-up in nite time of a solution of the Generalized Korteweg-de Vries equation arising from a perturbed unstable solitary wave is studied numerically. The computed solution is observed to blow-up in the L 1-norm in nite time by forming a spike of innnite height at x = x and at t = t. Scaled coordinates are introduced to examine the detailed structure of the solution in th...

We consider a system of coupled reaction-diffusion equations that models the interaction between multiple types of chemical species, particularly the interaction between one messenger RNA and different types of non-coding microRNAs in biological cells. We construct various modeling systems with different levels of complexity for the reaction, nonlinear diffusion, and coupled reaction and diffus...

Nonlinear system identification methods is a topic that has been gaining interest over the last years. One reason is the many application areas in controller design and system development. However, the problem of modeling nonlinear systems is complex and finding a general method that can be used for many different applications is difficult. This thesis treats recursive identification methods fo...