Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Recursive collocation for the numerical solution of stiff ordinary differential equations
HTML articles powered by AMS MathViewer

by H. Brunner PDF
Math. Comp. 28 (1974), 475-481 Request permission


The exact solution of a given stiff system of nonlinear (homogeneous) ordinary differential equations on a given interval I is approximated, on each subinterval ${\sigma _k}$ corresponding to a partition ${\pi _N}$ of I, by a linear combination ${U_k}(x)$ of exponential functions. The function ${U_k}(x)$ will involve only the "significant" eigenvalues (in a sense to be made precise) of the approximate Jacobian for ${\sigma _k}$. The unknown vectors in ${U_k}(x)$ are computed recursively by requiring that ${U_k}(x)$ satisfy the given system at certain suitable points in ${\sigma _k}$ (collocation), with the additional condition that the collection of these functions $\{ {U_k}\}$ represent a continuous function on I satisfying the given initial conditions.
    G. Bjurel et al., Survey of Stiff Ordinary Differential Equations, Report NA 70.11, Dept. of Computer Science, Royal Institute of Technology, Stockholm, 1970.
  • C. W. Gear, The automatic integration of stiff ordinary differential equations. , Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968) North-Holland, Amsterdam, 1969, pp. 187–193. MR 0260180
  • Wolfgang Hahn, Stability of motion, Die Grundlehren der mathematischen Wissenschaften, Band 138, Springer-Verlag New York, Inc., New York, 1967. Translated from the German manuscript by Arne P. Baartz. MR 0223668
  • J. D. Lambert, Computational methods in ordinary differential equations, John Wiley & Sons, London-New York-Sydney, 1973. Introductory Mathematics for Scientists and Engineers. MR 0423815
  • Werner Liniger and Ralph A. Willoughby, Efficient integration methods for stiff systems of ordinary differential equations, SIAM J. Numer. Anal. 7 (1970), 47–66. MR 260181, DOI 10.1137/0707002
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65L05
  • Retrieve articles in all journals with MSC: 65L05
Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Math. Comp. 28 (1974), 475-481
  • MSC: Primary 65L05
  • DOI:
  • MathSciNet review: 0347089