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Modern numerical methods for ordinary differential equations
Grant Hall,James Murray Watt +1 more
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This article is published in Mathematics of Computation.The article was published on 1978-10-01. It has received 421 citations till now. The article focuses on the topics: Numerical methods for ordinary differential equations & Numerical partial differential equations.read more
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A‐posteriori error estimates for the finite element method
Ivo Babuška,Werner C. Rheinboldt +1 more
TL;DR: In this article, a-posteriori error estimates for finite element solutions are derived in an asymptotic form for h 0 where h measures the size of the elements.
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Electron-positron pairs in physics and astrophysics: from heavy nuclei to black holes
TL;DR: In this article, a detailed review of the theoretical and experimental verification of the Dirac process and the Breit-Wheeler process is presented, together with a discussion of the possible verification of these processes.
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Electron-positron pairs in physics and astrophysics: from heavy nuclei to black holes
TL;DR: In this paper, the authors present a synthesis of theoretical, experimental and observational results originating from three fundametal physical processes: the critical electric field, the vacuum polarization process, and the gamma ray burst.
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Nonlinear adjustment of a thin annular film of viscous fluid surrounding a thread of another within a circular cylindrical pipe
TL;DR: In this paper, a nonlinear analysis based on lubrication theory is presented for the adjustment under surface tension of an initially uniform annular film of viscous fluid confined within a circular cylindrical pipe.
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The dynamics of runge–kutta methods
TL;DR: In this article, the authors attempt to elucidate the dynamics of the most commonly used family of numerical integration schemes, Runge-Kutta methods, by the application of the techniques of dynamical systems theory to the maps produced in the numerical analysis.