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Some $ A$-stable methods for stiff ordinary differential equations

Author: R. K. Jain
Journal: Math. Comp. 26 (1972), 71-77
MSC: Primary 65L05
MathSciNet review: 0303733
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Abstract: This paper gives some $ A$-stable methods of order $ 2n$, with variable coefficients, based on Hermite interpolation polynomials, for the stiff system of ordinary differential equations, making use of $ n$ starting values. The method is exact if the problem is of the form $ y'(t) = Py(t) + Q(t)$, where $ P$ is a constant and $ Q(t)$ is a polynomial of degree $ 2n$.

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  • [1] G. G. Dahlquist, ``A special stability problem for linear multistep methods,'' Nordisk Tidskr. Informations-Behandling, v. 3, 1963, pp. 27-43. MR 30 #715. MR 0170477 (30:715)
  • [2] C. E. Treanor, ``A method for the numerical integration of coupled first-order differential equations with greatly different time constants,'' Math. Comp., v. 20, 1966, pp. 39-45. MR 33 #889. MR 0192664 (33:889)
  • [3] S. P. Norsett, ``An $ A$-stable modification of the Adams-Bashforth methods,'' Conference on the Numerical Solution of Differential Equations (Dundee, Scotland, June 1969). MR 0267771 (42:2673)
  • [4] A. Ralston, A First Course In Numerical Analysis, McGraw-Hill, New York, 1965. MR 32 #8479. MR 0191070 (32:8479)
  • [5] C. W. Gear, Numerical Integration of Stiff Ordinary Differential Equations, Report #221, University of Illinois, Department of Computer Science, January 1967.
  • [6] P. Henrici, Discrete Variable Methods In Ordinary Differential Equations, Wiley, New York, 1962. MR 24 #B1772. MR 0135729 (24:B1772)

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Keywords: Stiff system of ordinary differential equations, $ A$-stability, multi-step methods, Lagrangian interpolation polynomials, Hermite interpolation polynomials
Article copyright: © Copyright 1972 American Mathematical Society

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