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Full-Text Articles in Applied Mathematics
Reaction Simulations: A Rapid Development Framework, Brendan Drake Donohoe
Reaction Simulations: A Rapid Development Framework, Brendan Drake Donohoe
Shared Knowledge Conference
Chemical Reaction Networks (CRNs) are a popular tool in the chemical sciences for providing a means of analyzing and modeling complex reaction systems. In recent years, CRNs have attracted attention in the field of molecular computing for their ability to simulate the components of a digital computer. The reactions within such networks may occur at several different scales relative to one another – at rates often too difficult to directly measure and analyze in a laboratory setting. To facilitate the construction and analysis of such networks, we propose a reduced order model for simulating such networks as a system of …
Two Applications Of High Order Methods: Wave Propagation And Accelerator Physics, Oleksii Beznosov
Two Applications Of High Order Methods: Wave Propagation And Accelerator Physics, Oleksii Beznosov
Shared Knowledge Conference
Numerical simulations of partial differential equations (PDE) are used to predict the behavior of complex physics phenomena when the real life experiments are expensive. Discretization of a PDE is the representation of the continuous problem as a discrete problem that can be solved on a computer. The discretization always introduces a certain inaccuracy caused by the numerical approximation. By increasing the computational cost of the numerical algorithm the solution can be computed more accurately. In the theory of numerical analysis this fact is called the convergence of the numerical algorithm. The idea behind high order methods is to improve the …