The purpose of this paper is twofold. Firstly we carry out an extension of the fully discrete third order TVD scheme, for linear case, presented in [8] to nonlinear scalar hyperbolic conservation laws for one and two dimensions. Secondly, we propose a semi-discrete version of the scheme. Time evolution is carried out by the third order TVD RungeKutta method. The advantages of the scheme are its...

In this paper we study the two-dimensional version of the RungeKutta Local Projection Discontinuous Galerkin (RKDG) methods, already defined and analyzed in the one-dimensional case. These schemes are defined on general triangulations. They can easily handle the boundary conditions, verify maximum principles, and are formally uniformly high-order accurate. Preliminary numerical results showing ...

Numerical solutions of the coupled Klein-Gordon-Schrödinger equations is obtained by using differential quadrature methods based on polynomials and quintic B-spline functions for space discretization and RungeKutta fourth order for time discretization. Stability of the schemes are studied using matrix stability analysis. The accuracy and efficiency of the methods are shown by conducting some nu...

In this paper, nonlinear dynamics of Duffing system with fractional order damping is investigated. The four order RungeKutta method and ten order CFE-Euler methods are introduced to simulate the fractional order Duffing equations. The effect of taking fractional order on the system dynamics is investigated using phase diagrams, bifurcation diagrams and Poincare map. The bifurcation diagram is a...

The flow and heat transfer characteristics of incompressible viscous flow over a nonlinearly stretching sheet with the presence of viscous dissipation is investigated numerically. The similarity transformation reduces the time-independent boundary layer equations for momentum and thermal energy into a set of coupled ordinary differential equations. The obtained equations, including nonlinear eq...

In this paper we discuss the use of stabilized Runge-Kutta methods to accelerate the solution of systems of nonlinear equations. The general idea is to seek solutions as steady state solutions of an associated system of ordinary differential equations. A class of stabilized RungeKutta methods are derived that can be used to efficiently evolve the associated system to steady state. Computational...

This demo provides a preview of a pre-release version of CyPhySim, an open-source simulator for cyber-physical systems. This simulator supports discrete-event models, quantized-state simulation of continuous dynamics, the Functional Mockup Interface (FMI), classical (RungeKutta) simulation of continuous dynamics, modal models (hybrid systems), discrete-time (periodic) systems, and algebraic loo...

There is resurging interest, in statistics and machine learning, in solvers for ordinary differential equations (ODEs) that return probability measures instead of point estimates. Recently, Conrad et al. introduced a sampling-based class of methods that are ‘well-calibrated’ in a specific sense. But the computational cost of these methods is significantly above that of classic methods. On the o...

The paper proposes a mechanical model of SFD-sliding bearing flexible rotor system, employing RungeKutta method to tackle nonlinear differential equation, thus acquiring the dynamic response and the unbalanced response curve. Results obtained show the route of flexible rotor system from stable periodic motion to chaos state is: periodic motion—quasi-periodic motion—chaos —period doubling bifurc...

In this paper, we have proposed and analyzed a nonlinear mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equations. Positive equilibrium points of the system are investigated and their stability analysis is carried out. Moreover, the numerical simulation of the proposed model is also performe...