The formal and empirical proof is that the ensemble of the learning models performs better than the single one. In order to construct the ensemble of the system of ordinary differential equations (ODEs), the two problems (diversity and accuracy of ODEs) are considered. In the paper, we estimate experimentally the model ensemble using multi-objective optimization. This paper presents a pareto op...

In this article, we present a continuation method, which transforms spatially distributed ordinary differential equation (ODE) systems into continuous partial (PDE). We show that can be performed for both linear and nonlinear systems, including multidimensional, space-varying, time-varying systems. When applied to large-scale network, the provides PDE describing evolution of continuous-state ap...

In this paper we propose a general method for a posteriori error estimation in the solution of initial value problems in ordinary differential equations (ODEs). With the help of adjoint sensitivity software, this method can be implemented efficiently. It provides a condition estimate for the ODE system. We also propose an algorithm for global error control, based on the condition of the system ...

In the present paper an analysis of mixed convection of an unsteady magneto hydrodynamic (MHD) flow of an incompressible viscous fluid through porous media due to a vertical porous stretching sheet in the presence of viscous dissipation, thermal radiation and heat source /sink has been carried out. The fluid considered is viscous and incompressible. The governing partial differential equations ...

General linear systems of delay differential-algebraic equations (DDAEs) of arbitrary order are studied in this paper. Under some consistency conditions, it is shown that every linear highorder DAE can be reformulated as an underlying high-order ordinary differential equation (ODE) and that every linear DDAE with single delay can be reformulated as a high-order delay differential equation (DDE)...

Validated Numerical Bounds on the Global Error for Initial Value Problems for Stiff Ordinary Differential Equations Chao Yu Master of Science Graduate Department of Computer Science University of Toronto 2004 There are many standard numerical methods for initial value problems (IVPs) for ordinary differential equations (ODEs). Compared with these methods, validated methods for IVPs for ODEs pro...

While purely numerical methods for solving ordinary differential equations (ODE), e.g., Runge–Kutta methods, are easy to implement, solvers that utilize analytical derivations of the right-hand side ODE, such as Taylor series method, outperform them in many cases. Nevertheless, method is not well-suited stiff problems since it explicit and A-stable. In our paper, we present a numerical-analytic...

In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to...

An ordinary differential equations (ODE) system describing the oscillation dynamics of a neuronal network is numerically integrated aiming to evidence chaos by the change in sign from negative to positive of the maximum Lyapunov exponents, and by a sudden decrease in the error doubling time. The error doubling time is calculated for different frequencies of the spiking rate oscillations. Than, ...

Bayesian parameter estimation in coupled ordinary differential equations (ODEs) is challenging due to the high computational cost of numerical integration. In gradient matching a separate data model is introduced with the property that its gradient may be calculated easily. Parameter estimation is then achieved by requiring consistency between the gradients computed from the data model and thos...