Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



Some new multistep methods for solving ordinary differential equations

Authors: G. K. Gupta and C. S. Wallace
Journal: Math. Comp. 29 (1975), 489-500
MSC: Primary 65L05
MathSciNet review: 0373290
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Three sets of linear multistep formulae for solving stiff and nonstiff ordinary differential equations are presented. Two of the sets are based on Adams-Moulton and stiff formulae used by Gear [1969]. A third set of formulae based on least-squares approximation is shown to be stiffly-stable up to order 8 and is suitable for solving stiff differential equations.

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

  • [G] G. DAHLQUIST (1956), "Convergence and stability in the numerical integration of ordinary differential equations," Math. Scand., v. 4, pp. 33-53. MR 18, 338. MR 0080998 (18:338d)
  • [G] G. DAHLQUIST (1963), "A special stability problem for linear multistep methods," BIT, v. 3, pp. 22-43. MR 30 #715. MR 0170477 (30:715)
  • [C] W. GEAR (1969), "The automatic integration of stiff ordinary differential equations," Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968), vol. 1: Mathematics, Software, North-Holland, Amsterdam, pp. 187-193. MR 41 #4808. MR 0260180 (41:4808)
  • [C] W. GEAR (1971a), "The automatic integration of ODE," Comm. ACM, v. 14, pp. 176-179. MR 0388778 (52:9612)
  • [C] W. GEAR (1971b), "Algorithm DIFSUB," Comm. ACM, v. 14, pp. 185-190. MR 0388778 (52:9612)
  • [G] K. GUPTA & C. S. WALLACE (1974), "A note about the stability and truncation error of linear multistep methods," SIAM J. Numer. Anal. (Submitted.)
  • [P] HENRICI (1962), Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York. MR 0135729 (24:B1772)
  • [N] MORRISON (1969), Introduction to Sequential Smoothing and Prediction, McGraw-Hill, New York.
  • [A] NORDSIECK (1962), "On numerical integration of ordinary differential equations," Math. Comp., v. 16, pp. 22-49. MR 24 #B2552. MR 0136519 (24:B2552)
  • [C] S. WALLACE & G. K. GUPTA (1973), "General multistep methods to solve ODE," Austral. Comput. J., v. 5, no. 2, pp. 62-69. MR 0362919 (50:15357)
  • [O] B. WIDLUND (1967), "A note on unconditionally stable linear multistep methods," BIT, V. 7, pp. 65-70. MR 35 #6373. MR 0215533 (35:6373)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65L05

Retrieve articles in all journals with MSC: 65L05

Additional Information

Keywords: Linear multistep methods, stiff differential equations, predictor-corrector methods, numerical solution of ordinary differential equations
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society