Implicit-explicit (IMEX) multistep methods are very useful for the time discretiza-tion of convection diffusion PDE problems such as the Burgers equations and also the incompressible Navier-Stokes equations. Semi-discretization in space of the latter typically gives rise to an index 2 differential-algebraic (DAE) system of equations. Runge-Kutta (RK) methods have been considered for the time di...

The solution of initial value problems of large systems of ordinary differential equations (ODEs) is computationally intensive and demands for efficient parallel solution techniques that take into account the complex architectures of modern parallel computer systems. This article discusses implementation techniques suitable for ODE systems with a special coupling structure, called limited acces...

Implicit-explicit (IMEX) Runge-Kutta (RK) schemes are popular high order time discretization methods for solving stiff kinetic equations. As opposed to the compressible Euler limit (leading order asymptotics of the Boltzmann equation as the Knudsen number ε goes to zero), their asymptotic behavior at the Navier-Stokes (NS) level (next order asymptotics) was rarely studied. In this paper, we ana...

Abstract— General linear methods (GLM) apply to a large family of numerical methods for ordinary differential equations, with RungeKutta (RK) and Almost Runge-Kutta (ARK) methods as two out of a number of special cases. In this paper, we have investigated the efficacy of Richardson extrapolation (RE) technique as a means of obtaining viable and acceptable estimates of the local truncation error...

In Xu [14], a class of parametrized flux limiters is developed for high order finite difference/volume essentially non-oscillatory (ENO) and Weighted ENO (WENO) schemes coupled with total variation diminishing (TVD) Runge-Kutta (RK) temporal integration for solving scalar hyperbolic conservation laws to achieve strict maximum principle preserving (MPP). In this paper, we continue along this lin...

We introduce a general framework for enforcing local or global maximum principles in high-order space-time discretizations of scalar hyperbolic conservation law. begin with sufficient conditions space discretization to be bound preserving (BP) and satisfy semi-discrete principle. Next, we propose monolithic convex (GMC) flux limiter which has the structure flux-corrected transport (FCT) algorit...

We analyze the behavior of an ensemble time integrators applied to semi-discrete problem resulting from spectral discretization equations describing Boussinesq thermal convection in a cylindrical annulus. The are cast their vorticity-streamfunction formulation that yields differential algebraic equation (DAE). comprises 28 members: 4 implicit-explicit multistep schemes, 22 Runge-Kutta (IMEX-RK)...

The context of this work is the development first order total variation diminishing (TVD) implicit-explicit (IMEX) Runge-Kutta (RK) schemes as a basis Multidimensional Optimal Order detection (MOOD) approach to approximate solution hyperbolic multi-scale equations. A key feature our newly proposed TVD that resulting CFL condition does not depend on fast waves considered model, long they are int...

Purpose: The aim of this article is focused on providing numerical solutions for system of second order robot arm problem using the Runge-Kutta Sixth order algorithm. Design/methodology/approach: The parameters governing the arm model of a robot control problem have also been discussed through RK-sixth-order algorithm. The precised solution of the system of equations representing the arm model ...