The numerical solution of second-order boundary value problems on nonuniform meshes

@article{Manteuffel1986TheNS,
  title={The numerical solution of second-order boundary value problems on nonuniform meshes},
  author={Thomas A. Manteuffel and Andrew B. White},
  journal={Mathematics of Computation},
  year={1986},
  volume={47},
  pages={511-535}
}
In this paper, we examine the solution of second-order, scalar boundary value problems on nonuniform meshes. We show that certain commonly used difference schemes yield second-order accurate solutions despite the fact that their truncation error is of lower order. This result illuminates a limitation of the standard stability, consistency proof of convergence for difference schemes defined on nonuniform meshes. A technique of reducing centered-difference approximations of first-order systems to… 

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