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


Authors: Thomas A. Manteuffel and Andrew B. White
Journal: Math. Comp. 47 (1986), 511-535, S53
MSC: Primary 65L10
DOI: https://doi.org/10.1090/S0025-5718-1986-0856700-3
MathSciNet review: 856700
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Abstract: 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 discretizations of the underlying scalar equation is developed. We treat both vertex-centered and cell-centered difference schemes and indicate how these results apply to partial differential equations on Cartesian product grids.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1986-0856700-3
Keywords: Boundary value problems, compact difference schemes, irregular grids, nonuniform mesh, difference quotients, truncation error
Article copyright: © Copyright 1986 American Mathematical Society