Revision of the theory of symmetric one-step methods for ordinary differential equations |
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Authors: | G Yu Kulikov |
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Institution: | 1. Department of Mathematics and Mechanics, Ulyanovsk State University, 432700, Ulyanovsk, Russia
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Abstract: | In this paper we develop a new theory of adjoint and symmetric methods in the class of general implicit one-step fixedstepsize methods. These methods arise from simple and natural definitions of the concepts of symmetry and adjointness that provide a fruitful basis for analysis. We prove a number of theorems for methods having these properties and show, in particular, that only the symmetric methods possess a quadratic asymptotic expansion of the global error. In addition, we give a very simple test to identify the symmetric methods in practice. |
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