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 $2n$.
- 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
- 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
- Syvert P. Nørsett, An $A$-stable modification of the Adams-Bashforth methods, Conf. on Numerical Solution of Differential Equations (Dundee, 1969) Springer, Berlin, 1969, pp. 214–219. MR 0267771
- Anthony Ralston, A first course in numerical analysis, McGraw-Hill Book Co., New York-Toronto-London, 1965. MR 0191070 C. W. Gear, Numerical Integration of Stiff Ordinary Differential Equations, Report #221, University of Illinois, Department of Computer Science, January 1967.
- Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons, Inc., New York-London, 1962. MR 0135729
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 71-77
- MSC: Primary 65L05
- DOI: https://doi.org/10.1090/S0025-5718-1972-0303733-1
- MathSciNet review: 0303733