Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

REVISION OF THE THEORY OF SYMMETRIC ONE-STEP METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS

  • Kulikov, G.Yo. (Department of Mathematics and mechanics Ulyanovsk State university)
  • Published : 1998.09.01

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Abstract

In this paper we develop a new theory of adjoint and symmetric method in the class of general implicit one-step fixed-stepsize methods. These methods arise from simple and natral def-initions of the concepts of symmetry and adjointness that provide a fruitful basis for analysis. We prove a number of theorems for meth-ods 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.

Keywords

References

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