Numerical stability is considered for several Runge-Kutta methods to systems of neutral delay differential equations. The linear stability analysis is adopted to the system. Adapted with the equistage interpolation process as well as the continuous extension, the Runge-Kutta methods are shown to have the numerical stability similar to the analytical asymptotic stability with arbitrary stepsize,...

Galerkin fully discrete approximations for parabolic equations with time-dependent coefficients are analyzed. The schemes are based on implicit Runge-Kutta methods, and are coupled with preconditioned iterative methods to approximately solve the resulting systems of linear equations. It is shown that for certain classes of Runge-Kutta methods, the fully discrete equations exhibit parallel featu...

In this paper, differential transform method (DTM) is described and is applied to solve systems of nonlinear ordinary differential equations which is arising in HIV infections of cell. Intervals of validity of the solution will be extended by using Pade approximation. The results also will be compared with those results obtained by Runge-Kutta method. The technique is described and is illustrat...

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...

Explicit Runge–Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge–Kutta schemes available in literature. Furthermore, they have a small principal error n...

Abstract. This paper develops Runge-Kutta PK-based central discontinuous Galerkin (CDG) methods with WENO limiter to the oneand two-dimensional special relativistic hydrodynamical (RHD) equations, K = 1,2,3. Different from the non-central DG methods, the Runge-Kutta CDG methods have to find two approximate solutions defined on mutually dual meshes. For each mesh, the CDG approximate solutions o...