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On Error Estimation in Runge-Kutta MethodsKeywords: Error , Estimation , Runge-Kutta , Richardson Extrapolation , Exact , Approximate Abstract: The increase in PCs' capabilities and communication bandwidth over the last decade has made distributed computing a more practical idea for solving computational problems. We have developed a decentralized P2P system called ParCop (Parallel Cooperation). ParCop enables each peer in a P2P network to view the rest of the network as a supercomputer, by running ParCop system software on the machine as a daemon service. ParCop allows participants to execute different applications on shared resources owned by other participants. In this paper, we present the new capabilities of ParCop system: efficient resource discovery by using the Blackboard Resource Discovery Mechanism (BRDM), adaptation in dynamic networks, effective data caching, efficient scaling and the provision of a secure environment. We also present three scheduling policies that allow peers in ParCop environment to take scheduling decisions based on the information coming from the peers in the network. The use of these scheduling policies minimizes the processing time of applications in ParCop, improves the ability of dealing with peers which have different capabilities and requirements, and achieves efficient load balancing.
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