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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Integrating ODEs in the complex plane—pole vaulting
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by George F. Corliss PDF
Math. Comp. 35 (1980), 1181-1189 Request permission

Abstract:

Most existing algorithms for solving initial value problems in ordinary differential equations implicitly assume that all variables are real. If the real-valued assumption is removed, the solution can be extended by analytic continuation along a path of integration in the complex plane of the independent variable. This path is chosen to avoid singularities which can make the solution difficult or impossible for standard methods. We restrict our attention to Taylor series methods, although other methods can be suitably modified. Numerical examples are given for (a) singularities on the real axis, (b) singularities in derivatives higher than those involved in the differential equation, and (c) singularities near the real axis. These examples show that the pole vaulting method merits further study for some special problems for which it is competitive with standard methods.
References
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1181-1189
  • MSC: Primary 65L05; Secondary 34A20
  • DOI: https://doi.org/10.1090/S0025-5718-1980-0583495-8
  • MathSciNet review: 583495