Abstract
Many numerical methods used to solve Ordinary Differential Equations, or Differential Algebraic Equations can be written as general linear methods. The B-convergence results for general linear methods are for algebraically stable methods, and therefore useless for nearly A-stable methods. The purpose of this paper is to show convergence for singular perturbation problems for the class of general linear methods without assuming A-stability.
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Schneider, S. Convergence results for general linear methods on singular perturbation problems. BIT 33, 670–686 (1993). https://doi.org/10.1007/BF01990542
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DOI: https://doi.org/10.1007/BF01990542