Numerical Algorithms

, Volume 71, Issue 1, pp 139–150 | Cite as

Analysis of some numerical methods on layer adapted meshes for singularly perturbed quasilinear systems

Original Paper

Abstract

We consider a coupled system of first-order singularly perturbed quasilinear differential equations with given initial conditions. The leading term of each equation is multiplied by a distinct small positive parameter, which induces overlapping layers. The quasilinear system is discretized by using first and second order accurate finite difference schemes for which we derive general error estimates in the discrete maximum norm. As consequences of these error estimates we establish nodal convergence of O((N−1 lnN)p),p=1,2, on the Shishkin mesh and O(Np),p=1,2, on the Bakhvalov mesh, where N is the number of mesh intervals and the convergence is robust in all of the parameters. Numerical computations are included which confirm the theoretical results.

Keywords

Singular perturbation Coupled system Robust numerical method Layer-adapted meshes 

Mathematics Subject Classification (2010)

65L05 65L11 65L12 65L70 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.CMUC, Department of MathematicsUniversity of CoimbraCoimbraPortugal
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  3. 3.Max Planck Institute for Solar System ResearchGöttingenGermany

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