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Christopher D. Marcotte, Roman O. Grigoriev
Graphical processing units (GPUs) promise to revolutionize scientific computing in the near future. Already, they allow almost real-time integration of simplified numerical models of cardiac tissue dynamics. However, the integration methods that have been developed so far are typically of low order and use single precision arithmetics. In this work, we describe numerical implementation of […]
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Saurabh Maniktala, Anisha Goel, A. B. Patki, R. C. Meharde
In the present era Chaos theory has tremendous potential in Computer Science Domain. The true potential of Chaos theory can be realized with the assistance of high performance computing aids such as GPU that have become available in present times. The main purpose is to develop a high performance experimental laboratory in academic institutions, for […]
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Scott A. Sarra, Clyde Meador
Multiple results in the literature exist that indicate that all computed solutions to chaotic dynamical systems are time-step dependent. That is, solutions with small but different time steps will decouple from each other after a certain (small) finite amount of simulation time. When using double precision floating point arithmetic time step independent solutions have been […]
A. Seibert, S. Denisov, Alexey V. Ponomarev, P. Hanggi
The Arnold diffusion constitutes a dynamical phenomenon which may occur in the phase space of a non-integrable Hamiltonian system whenever the number of the system degrees of freedom is M>=3. The diffusion is mediated by a web-like structure of resonance channels, which penetrates the phase space and allows the system to explore the whole energy […]
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J.R. Seaton, J.C Sprott
In this study, chaotic partial differential equations (PDEs) were numerically solved using a parallel algorithm on graphics processing units (GPU). This new method will aid in our search for simple examples of chaotic PDEs. Computational time using the GPU was compared to other languages such as Matlab and PowerBASIC. The GPU algorithm was optimized using […]
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Karsten Ahnert, Mario Mulansky
Many physical, biological or chemical systems are modeled by ordinary differential equations (ODEs) and finding their solution is an every-day-task for many scientists. Here, we introduce a new C++ library dedicated to find numerical solutions of initial value problems of ODEs: odeint (www.odeint.com). odeint is implemented in a highly generic way and provides extensive interoperability […]
A. Seibert, S. Denisov, Alexey V. Ponomarev, P. Hanggi
The Arnold diffusion constitutes a dynamical phenomenon which may occur in the phase space of a non-integrable Hamiltonian system whenever the number of the system degrees of freedom is $M geq 3$. The diffusion is mediated by a web-like structure of resonance channels, which penetrates the phase space and allows the system to explore the […]
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