Introduction PACT Abstract A parallel implementation for multi-implicit Runge-Kutta methods with real eigen-values is described. The parallel method is analysed and the algorithm is devised. For the problem with d domains, the amount within the s-stage Runge-Kutta method, associated with the solution of system, is proportional to (sd) 3. The proposed parallelisation transforms the above system ...

We present software packages for the holonomic gradient method (HGM). These packages compute normalizing constants and the probabilities of some regions. While many algorithms which compute integrals over high-dimensional regions utilize the Monte-Carlo method, our HGM utilizes algorithms for solving ordinary differential equations such as the Runge-Kutta-Fehlberg method. As a result, our HGM c...

In this paper we study a class of explicit pseudo two-step Runge-Kutta (EP-TRK) methods for rst-order ODEs for parallel computers. We investigate linear stability and derive methods with enlarged stability regions. In numerical experiments on a shared memory computer we compare a parallel variable step size EPTRK implementation with the eecient sequential Runge-Kutta method dopri5.

Article history: Received 31 January 2008 Received in revised form 18 June 2008 Accepted 23 July 2008 Available online 19 August 2008

Abstract In this paper, third-order 3-stage diagonally implicit Runge–Kutta–Nystrom method embedded in fourthorder 4-stage for solving special second-order initial value problems is constructed. The method has the property of minimized local truncation error as well as the last row of the coefficient matrix is equal to the vector output. The stability of the method is investigated and a standar...

Spectral deferred correction is a flexible technique for constructing high-order, stiffly-stable time integrators using a low order method as a base scheme. Here we examine their use in conjunction with splitting methods to solve initial-boundary value problems for partial differential equations. We exploit their close connection with implicit Runge–Kutta methods to prove that up to the full ac...