×

An implicit two-point numerical integration formula for linear and nonlinear stiff systems of ordinary differential equations. (English) Zbl 0383.65044


MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L07 Numerical investigation of stability of solutions to ordinary differential equations
65D30 Numerical integration
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] S. O. FATUNLA, ”A new semi-implicit integration algorithm to cope with stiff systems of ordinary differential equations,” Manuscript, 1976.
[2] K. M. BROWN, ”A quadratically convergent Newton-like method based upon Gaussian elimination,” Math. Comp., v. 20, 1966, pp. 11-20.
[3] J. D. Lambert, Nonlinear methods for stiff systems of ordinary differential equations, Conference on the Numerical Solution of Differential Equations (Univ. of Dundee, Dundee, 1973) Springer, Berlin, 1974, pp. 75 – 88. Lecture Notes in Math., Vol. 363.
[4] Leon Lapidus and John H. Seinfeld, Numerical solution of ordinary differential equations, Mathematics in Science and Engineering, Vol. 74, Academic Press, New York-London, 1971. · Zbl 0217.21601
[5] 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. · Zbl 0183.18103 · doi:10.1147/rd.115.0537
[6] Werner Liniger and Ralph A. Willoughby, Efficient integration methods for stiff systems of ordinary differential equations, SIAM J. Numer. Anal. 7 (1970), 47 – 66. · Zbl 0187.11003 · doi:10.1137/0707002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.