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...

In this paper, numerical spline-based differential quadrature is presented for solving the boundary and initial value problems, and its application is used to solve the fixed rectangular membrane vibration equation. For the time integration of the problem, the Runge–Kutta and spline-based differential quadrature methods have been applied. The Runge–Kutta method was unstable for solving the prob...

In this paper, we consider the parallel solution of nonstii ordinary diierential equations with two diierent classes of Runge-Kutta (RK) methods providing embedded solutions: classical embedded RK methods and iterated RK methods which were constructed especially for parallel execution. For embedded Runge-Kutta methods, mainly the potential system parallelism is exploited. Iterated RK methods pr...

Is a complex space X which is the union of an increasing sequence X1 ⊂ X2 ⊂ X3 ⊂ · · · of open Stein subspaces itself a Stein space ? From the begining this question has held great interest in Stein theory. The special case when {Xj}j≥1 is a sequence of Stein domains in I C n had been proved long time ago by Behnke and Stein [2]. In 1956, Stein [13] answered positively the question under the ad...

The Pommiez operator (∆ f )(z) = ( f (z)− f (0))/z is considered in the space (G) of the holomorphic functions in an arbitrary finite Runge domain G. A new proof of a representation formula of Linchuk of the commutant of ∆ in (G) is given. The main result is a representation formula of the commutant of the Pommiez operator in an arbitrary invariant hyperplane of (G). It uses an explicit convolu...

This paper presents a novel way of identifying and illustrating the accuracy in the particle tracing method for ow visualization. We make use of explicit Runge-Kutta methods for particle tracing in steady velocity elds, and describe three approaches to estimate the accuracy of the calculated path. These approaches are: reintegration (with smaller tolerance or in a backward direction), global er...