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.

 

An attempt to avoid exact Jacobian and nonlinear equations in the numerical solution of stiff differential equations
HTML articles powered by AMS MathViewer

by Trond Steihaug and Arne Wolfbrandt PDF
Math. Comp. 33 (1979), 521-534 Request permission

Abstract:

A class of linear implicit methods for numerical solution of stiff ODE’s is presented. These require only occasional calculation of the Jacobian matrix while maintaining stability. Especially, an effective second order stable algorithm with automatic stepsize control is designed and tested.
References
  • R. England, Error estimates for Runge-Kutta type solutions to systems of ordinary differential equations, Comput. J. 12 (1969/70), 166–170. MR 242377, DOI 10.1093/comjnl/12.2.166
  • W. H. ENRIGHT, T. E. HULL & B. LINDBERG, "Comparing numerical methods for stiff systems of o.d.e.:s," BIT, v. 15, 1975, pp. 1-10.
  • C. William Gear, Numerical initial value problems in ordinary differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR 0315898
  • S. P. NØRSETT, Semi-Explicit Runge-Kutta Methods, Technical Report 6, Dept. of Math., Univ. of Trondheim, 1974.
  • Syvert P. Nørsett and Arne Wolfbrandt, Attainable order of rational approximations to the exponential function with only real poles, Nordisk Tidskr. Informationsbehandling (BIT) 17 (1977), no. 2, 200–208. MR 447900, DOI 10.1007/bf01932291
  • A. WOLFBRANDT, A Study of Rosenbrock Processes with Respect to Order Conditions and Stiff Stability, Thesis, Chalmers Univ. of Technology, Goteborg, Sweden, 1977.
  • Arne Wolfbrandt, A note on a recent result of rational approximations to the exponential function, Nordisk Tidskr. Informationsbehandling (BIT) 17 (1977), no. 3, 367–368. MR 464551, DOI 10.1007/bf01932159
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65L05
  • Retrieve articles in all journals with MSC: 65L05
Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Math. Comp. 33 (1979), 521-534
  • MSC: Primary 65L05
  • DOI: https://doi.org/10.1090/S0025-5718-1979-0521273-8
  • MathSciNet review: 521273