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Grid Oscillations in Finite-Difference Scheme and a Method for Their Approximate Analysis

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The study focuses on the phenomenon of short-wave (sawtooth) oscillations manifested in some discrete approximations of hyperbolic systems of equations. A technique for the analysis of oscillations is proposed, decomposing the solution into a “smooth” and a “sawtooth” components, followed by application of the known differential approximation method. The new method makes it possible to assess the properties of initial–boundary-value problems and spectral finite-difference problems. The central-difference scheme for the transport equation is investigated in detail, using various boundary conditions that can be optimized. Possible generalizations of the approach to multidimensional and nonlinear problems are suggested.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    L. V. Dorodnitsyn

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  1. L. V. Dorodnitsyn
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Correspondence to L. V. Dorodnitsyn.

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Translated from Prikladnaya Matematika i Informatika, No. 50, 2015, pp. 93–112.

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Dorodnitsyn, L.V. Grid Oscillations in Finite-Difference Scheme and a Method for Their Approximate Analysis. Comput Math Model 27, 472–488 (2016). https://doi.org/10.1007/s10598-016-9337-y

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  • DOI: https://doi.org/10.1007/s10598-016-9337-y

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