Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



Recursive collocation for the numerical solution of stiff ordinary differential equations

Author: H. Brunner
Journal: Math. Comp. 28 (1974), 475-481
MSC: Primary 65L05
MathSciNet review: 0347089
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: 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.

References [Enhancements On Off] (What's this?)

  • [1] G. Bjurel et al., Survey of Stiff Ordinary Differential Equations, Report NA 70.11, Dept. of Computer Science, Royal Institute of Technology, Stockholm, 1970.
  • [2] 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
  • [3] Wolfgang Hahn, Stability of motion, Translated from the German manuscript by Arne P. Baartz. Die Grundlehren der mathematischen Wissenschaften, Band 138, Springer-Verlag New York, Inc., New York, 1967. MR 0223668
  • [4] 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
  • [5] 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 0260181,

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65L05

Retrieve articles in all journals with MSC: 65L05

Additional Information

Keywords: System of stiff nonlinear homogeneous ordinary differential equations, approximate solution by sums of exponential functions, recursive collocation, one-step methods
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society