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Statistical moments for solutions of non-linear scalar equations with random Riemann data

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  • Conceição, D.
  • Lambert, W.

Abstract

In this paper we generalize the solution of random Riemann problem for a scalar equation, for flux function with one inflection point. We introduce both a bifurcation theory for the state space (uL, uR) and an efficient numerical method. The statistical moments are obtained from a computable integral exact form. We present some numerical results, considering an uniform distribution, and a bivariate normal distribution. We obtain very good results compared with the solution obtained with Monte Carlo.

Suggested Citation

  • Conceição, D. & Lambert, W., 2015. "Statistical moments for solutions of non-linear scalar equations with random Riemann data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 107(C), pages 120-133.
    • Handle: RePEc:eee:matcom:v:107:y:2015:i:c:p:120-133
    DOI: 10.1016/j.matcom.2014.05.004
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    References listed on IDEAS

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    1. Cunha, M. Cristina C. & Dorini, Fábio A., 2009. "Statistical moments of the solution of the random Burgers–Riemann problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1440-1451.
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