We present a new variational characterization of breather solutions any equation the focusing Gardner hierarchy. This hierarchy is characterized by nonnegative index n, and 2n + 1 represents order corresponding PDE member. In this paper, we first show existence such breathers, that they are (2n+1)th-order equation. Then prove universality property, in sense all these satisfy same fourth station...

We describe the ARKODE library of one-step time integration methods for ordinary differential equation (ODE) initial-value problems (IVPs). In addition to providing standard explicit and diagonally implicit Runge--Kutta methods, also supports designed treat additive splittings IVP, including implicit-explicit (ImEx) multirate infinitesimal (MRI) methods. present role within SUNDIALS suite nonli...

The purpose of this work is to introduce a new idea how avoid the factorization large matrices during solution stiff systems ODEs. Starting from general form an explicit linear multistep method we suggest adaptively choose its coefficients on each integration step in order minimize norm residual implicit BDF formula. Thereby reduce number unknowns n O(1), where dimension ODE system. We call typ...

We present a framework for the interactive simulation of surgical cuts such as being practiced in surgical treatment. Unlike most existing methods our framework is based on tetrahedral volume meshes providing more topological flexibility. In order to keep the representation consistent we apply adaptive subdivision schemes dynamically during the simulation. The detection of collisions between th...

Recently an implicit method has been presented for solving first order singular initial value problem. The method is extended to solve second or higher order problems having a singular point. The method presents more correct result than those obtained by the implicit Euler and second order implicit Runge-Kutta (RK2) methods. The method is illustrated by suitable examples.

Implicit Leadership Theories (ILTs) are individuals’ perceptions of the traits and behaviors characterizing leaders. Four studies investigated the reliabilities and different types of validities for a scale developed to measure Iranian Implicit leadership Theories (IILTs). Study 1 used a qualitative method to extract the implicit theories of ideal leadership after interviewing 27 experts. The I...

The second order Ordinary Differential Equation (ODE) system obtained after semidiscretizing the wavetype Partial Differential Equation (PDE) with the Finite Element Method (FEM), shows strong numerical stiffness. Although it can be integrated using Matlab ode-solvers, the function ode15s offered by Matlab for solving stiff ODE systems does not result very efficient as its resolution requires t...

A popular approach for the numerical solution of boundary value ODE problems involves the use of collocation methods. Such methods can be naturally implemented so as to provide a continuous approximation to the solution over the entire problem interval. On the other hand, several authors have suggested as an alternative, certain subclasses of the implicit Runge-Kutta formulas, known as mono-imp...

We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of Structural Causal Models, especially for cyclic models.

This contribution presents development and trends of simulation software, from the simple structures for ‘static’ explicit ODE models to modelling of structural dynamic systems with DAEs. Simulation emerged in the 1960’ in order to be able to analyse nonlinear dynamic system and to synthesize nonlinear control systems. Since that time simulation as problem solving tool has been developed toward...