In this paper we design and apply new embedded pairs of Fractional Step Runge-Kutta methods to the efficient resolution of multidimensional parabolic problems. These time integrators are combined with a suitable splitting of the elliptic operator subordinated to a decomposition of the spatial domain and a standard spatial discretization. With this technique we obtain parallel algorithms which h...

The present paper deals with the study of fluid flow and heat transfer characteristics occurring during the melting process due to a stretching surface in micropolar fluid with thermal radiation. A uniform magnetic field is applied normal to surface. The governing equations representing fluid flow have been transformed into nonlinear ordinary differential equations using similarity transformati...

The high-order accurate Runge-Kutta discontinuous Galerkin (RKDG) method is applied to the simulation of compressible multi-medium flow, generalizing the interface treating method given in [9]. In mixed cells, where the interface is located, Riemann problems are solved to define the states on both sides of the interface. The input states to the Riemann problem are obtained by extrapolation to t...

A fourth-order, implicit, low-dispersion, and low-dissipation Runge-Kutta scheme is introduced. The scheme is optimized for minimal dissipation and dispersion errors. High order accuracy is achieved with fewer stages than standard explicit Runge-Kutta schemes. The scheme is designed to be As table for highly stiff problems. Possible applications include wall-bounded flows with solid boundaries ...

Embedded Runge-Kutta methods are among the most popular methods for the solution of non-stiff initial value problems of ordinary differential equations (ODEs). We investigate the use of load balancing strategies in a dataparallel implementation of embedded Runge-Kutta integrators. Since the parallelism contained in the function evaluation of the ODE system is typically very fine-grained, our ai...

The condition equations are derived by the introduction of a system of equivalent differential equations, avoiding the usual formalism with trees and elementary differentials. Solutions to the condition equations are found by direct numerical optimization, during which simplifying assumptions upon the Runge-Kutta coefficients may or may not be used. Depending on the optimization criterion, diff...

Systems of functional-diierential and functional equations occur in many biological, control and physics problems. They also include functional diierential equations of neutral type as special cases. In this paper we present a numerical method that is based on the continuous extension of the Runge{Kutta method (for ordinary diierential equations) and the collocation method (for functional equat...

Two techniques for reliably controlling the defect (residual) in the numerical solution of nonstiff initial value problems were given in [D. This work describes an alternative approach based on Hermite-Birkhoff interpolation. The new approach has two main advantagesmit is applicable to Runge-Kutta schemes of any order, and it gives rise to a defect of the optimum asymptotic order of accuracy. F...