Numerical Algorithms

, Volume 77, Issue 4, pp 1117–1139 | Cite as

A numerical method for stationary shock problems with monotonic solutions

  • Relja Vulanović
  • Thái Anh Nhan
Original Paper


Numerical methods are considered for singularly perturbed quasilinear problems having interior-shock solutions. It is shown that the direct discretization on a layer-adapted mesh is ineffective for these problems. A special method is proposed for the case when the solution is monotonic: the problem is transformed by interchanging the dependent and independent variables, and it is then discretized on a uniform mesh. The method is analyzed both theoretically and numerically. It is shown that it can be effective, but that it is not entirely without problems. An approach for improving the method is suggested.


Quasilinear boundary value problem Singular perturbation Interior shock Finite differences 

Mathematics Subject Classification (2010)

65L10 65L11 65L12 65L20 


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Thanks are due to two anonymous reviewers whose comments helped us improve the paper.


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Mathematical SciencesKent State University at StarkNorth CantonUSA
  2. 2.Department of MathematicsOhlone CollegeFremontUSA

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