Matricial difference schemes for integrating stiff systems of ordinary differential equations
HTML articles powered by AMS MathViewer
- by W. L. Miranker PDF
- Math. Comp. 25 (1971), 717-728 Request permission
Abstract:
In this paper we give a description and analysis of a class of matricial difference schemes. This class of schemes is based in part on a generalization of the feature of classical numerical methods of being characterized by approximations at a single point in the complex plane. The schemes introduced here are effective for integrating stiff systems.References
- 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
- M. E. Fowler and R. M. Warten, A numerical integration technique for ordinary differential equations with widely separated eigenvalues, IBM J. Res. Develop. 11 (1967), 537–543. MR 216757, DOI 10.1147/rd.115.0537
- C. F. Curtiss and J. O. Hirschfelder, Integration of stiff equations, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 235–243. MR 47404, DOI 10.1073/pnas.38.3.235
- Charles E. Treanor, A method for the numerical integration of coupled first-order differential equations with greatly different time constants, Math. Comp. 20 (1966), 39–45. MR 192664, DOI 10.1090/S0025-5718-1966-0192664-3
- J. Certaine, The solution of ordinary differential equations with large time constants, Mathematical methods for digital computers, Wiley, New York, 1960, pp. 128–132. MR 0117917
- Willard L. Miranker and Werner Liniger, Parallel methods for the numerical integration of ordinary differential equations, Math. Comp. 21 (1967), 303–320. MR 223106, DOI 10.1090/S0025-5718-1967-0223106-8
- Germund G. Dahlquist, A special stability problem for linear multistep methods, Nordisk Tidskr. Informationsbehandling (BIT) 3 (1963), 27–43. MR 170477, DOI 10.1007/bf01963532 C. W. Gear, Numerical Integration of Stiff Ordinary Differential Equations, Dept. of Computer Science, Report #221, University of Illinois, Urbana, Illinois. W. L. Miranker, Difference Schemes for the Integration of Stiff Systems of Ordinary Differential Equations, IBM Research Center, Report #RC-1977, 1968. F. R. Gantmacher, The Theory of Matrices, GITTL, Moscow, 1953; English transl., Chelsea, New York, 1959. MR 16, 438.
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Math. Comp. 25 (1971), 717-728
- MSC: Primary 65L05
- DOI: https://doi.org/10.1090/S0025-5718-1971-0301939-8
- MathSciNet review: 0301939