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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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The application of Runge-Kutta schemes to singular initial value problems
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by Frank de Hoog and Richard Weiss PDF
Math. Comp. 44 (1985), 93-103 Request permission

Abstract:

A theory for explicit Runge-Kutta schemes applied to the initial value problem for a first-order system of differential equations with a singularity of the first kind is developed. It is shown that, in general, the order of convergence is at most two but that the usual order up to a logarithmic term can be obtained for level three and four schemes applied to specific problems.
References
  • Louis Bauer, Edward L. Reiss, and Herbert B. Keller, Axisymmetric buckling of hollow spheres and hemispheres, Comm. Pure Appl. Math. 23 (1970), 529–568. MR 278605, DOI 10.1002/cpa.3160230402
  • Frank R. de Hoog and Richard Weiss, Difference methods for boundary value problems with a singularity of the first kind, SIAM J. Numer. Anal. 13 (1976), no. 5, 775–813. MR 440931, DOI 10.1137/0713063
    • F. de Hoog & R. Weiss, "The application of linear multistep methods to singular initial value problems," Math. Comp., v. 31, 1977, pp. 676-690.
  • Herbert B. Keller and Antoinette W. Wolfe, On the nonunique equilibrium states and buckling mechanism of spherical shells, J. Soc. Indust. Appl. Math. 13 (1965), 674–705. MR 183174
    • H. Meissner & P. Tholfsen, "Cylindrically symmetric solutions of the Ginzburg-Landau equations," Phys. Rev., v. 169, 1968, pp. 413-416. S. V. Parter, M. L. Stein & P. R. Stein, On the Multiplicity of Solutions of a Differential Equation Arising in Chemical Reactor Theory, Computer Sciences Technical Report #194, University of Wisconsin-Madison, 1973.
  • P. Rentrop, A Taylor series method for the numerical solution of two-point boundary value problems, Numer. Math. 31 (1978/79), no. 4, 359–375. MR 516580, DOI 10.1007/BF01404566
  • Anthony Ralston, A first course in numerical analysis, McGraw-Hill Book Co., New York-Toronto-London, 1965. MR 0191070
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Math. Comp. 44 (1985), 93-103
  • MSC: Primary 65L05
  • DOI: https://doi.org/10.1090/S0025-5718-1985-0771033-0
  • MathSciNet review: 771033