Some new high-order multistep formulae for solving stiff equations

Author:
G. K. Gupta

Journal:
Math. Comp. **30** (1976), 417-432

MSC:
Primary 65L05

DOI:
https://doi.org/10.1090/S0025-5718-1976-0423812-1

MathSciNet review:
0423812

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Several new multistep formulae of orders up to 9 for solving stiff ordinary differential equations are presented. Results of numerical testing of these new formulae and some formulae presented in earlier papers and the stiff formulae used by Gear are included.

**[1]**W. H. ENRIGHT, T. E. HULL & B. LINDBERG, "Comparing numerical methods for stiff systems of O.D.E.'s,"*BIT*, v. 15, 1975, pp. 10-48.**[2]**W. H. Enright,*Second derivative multistep methods for stiff ordinary differential equations*, SIAM J. Numer. Anal.**11**(1974), 321–331. MR**0351083**, https://doi.org/10.1137/0711029**[3]**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****[4]**C. W. GEAR, "Algorithm 407-DIFSUB for solution of ordinary differential equations,"*Comm. ACM*, v. 14, 1971, pp. 185-190.**[5]**G. K. Gupta and C. S. Wallace,*Some new multistep methods for solving ordinary differential equations*, Math. Comp.**29**(1975), 489–500. MR**0373290**, https://doi.org/10.1090/S0025-5718-1975-0373290-5**[6]**Peter Henrici,*Discrete variable methods in ordinary differential equations*, John Wiley & Sons, Inc., New York-London, 1962. MR**0135729****[7]**T. E. Hull, W. H. Enright, B. M. Fellen, and A. E. Sedgwick,*Comparing numerical methods for ordinary differential equations*, SIAM J. Numer. Anal.**9**(1972), 603–637; errata, ibid. 11 (1974), 681. MR**0351086**, https://doi.org/10.1137/0709052**[8]**F. T. KROGH, "On testing a subroutine for the numerical integration of ordinary differential equations,"*J. ACM*, v. 20, 1973, pp. 545-562.**[9]**Bengt Lindberg,*On smoothing and extrapolation for the trapezoidal rule*, Nordisk Tidskr. Informationsbehandling (BIT)**11**(1971), 29–52. MR**0281356****[10]**N. MORRISON,*Introduction to Sequential Smoothing and Prediction*, McGraw-Hill, New York, 1969.**[11]**C. S. Wallace and G. K. Gupta,*General linear multistep methods to solve ordinary differential equations*, Austral. Comput. J.**5**(1973), 62–69. MR**0362919****[12]**Olof B. Widlund,*A note on unconditionally stable linear multistep methods*, Nordisk Tidskr. Informations-Behandling**7**(1967), 65–70. MR**0215533**

Retrieve articles in *Mathematics of Computation*
with MSC:
65L05

Retrieve articles in all journals with MSC: 65L05

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1976-0423812-1

Keywords:
Linear multistep methods,
stiff differential equations,
numerical solution of ODE

Article copyright:
© Copyright 1976
American Mathematical Society