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A -Stable Composite Multistep Methods
Journal of the ACM, 1973Consider the set of multistep formulas ∑ l -1 j mn - k α ij x mn + j
Harry M. Sloate, Theodore A. Bickart
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Multistep Methods With Modified Predictors and Correctors
Journal of the ACM, 1967In April, 1964, Gragg and Stetter published a set of numerical methods for solving y′ = f ( x , y ) which rely on some very accurate correctors, using a “nonstep” point within the interval of integration.
John J. Kohfeld, Gene Thomas Thompson
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Generalized Multistep Predictor-Corrector Methods
Journal of the ACM, 1964The order p which is obtainable with a stable k -step method in the numerical solution of y′ = f ( x , y ) is limited to p = k + 1 by the theorems of
William B. Gragg, Hans J. Stetter
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SIAM Journal on Numerical Analysis, 1983
The properties and possibilities of one-leg methods are presented in a manner that admits the generalization to smoothly varying step size. A new definition is given of the local truncation error and of the order of consistency. Some data are given for the most accurate one-leg methods, i.e.
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The properties and possibilities of one-leg methods are presented in a manner that admits the generalization to smoothly varying step size. A new definition is given of the local truncation error and of the order of consistency. Some data are given for the most accurate one-leg methods, i.e.
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1996
The search for higher order A -stable multistep methods is carried out in two main directions: Use higher derivatives of the solutions; Throw in additional stages, off-step points, super-future points and the like, which leads into the large field of general linear methods.
Ernst Hairer, Gerhard Wanner
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The search for higher order A -stable multistep methods is carried out in two main directions: Use higher derivatives of the solutions; Throw in additional stages, off-step points, super-future points and the like, which leads into the large field of general linear methods.
Ernst Hairer, Gerhard Wanner
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Auxiliary linear multistep methods: explicit
International Journal of Computer Mathematics, 1989A class of high order explicit 2-step methods for the integration of ordinary differential equations have been developed. The methods use the slopes at several auxiliary points within a step. The efficiency of the methods has been established by comparing numerical results with those of Adams—Bashforth—Moulton predictor-corrector method and Runge-Kutta
G. Sahoo, N. Datta
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Stability of Multistep Methods
1996A general k-step multistep method is of the form $${\alpha _k}{y_{m + k}} + {\alpha _{k - 1}}{y_{m + k - 1}} + \ldots + {\alpha _0}{y_m} = h\left( {{\beta _k}{f_{m + k}} + \ldots + {\beta _0}{f_m}} \right).$$ (1.1)
Ernst Hairer, Gerhard Wanner
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2002
Multistep methods are the basis of important codes for nonstiff differential equations (Adams methods) and for stiff problems (BDF methods). We study here their applicability to long-time integrations of Hamiltonian or reversible systems.
Ernst Hairer +2 more
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Multistep methods are the basis of important codes for nonstiff differential equations (Adams methods) and for stiff problems (BDF methods). We study here their applicability to long-time integrations of Hamiltonian or reversible systems.
Ernst Hairer +2 more
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On convergent linear multistep matrix methods
International Journal of Computer Mathematics, 1991In this paper a sufficient condition in order to a linear multistep matrix method for computing numerically initial value differential matrix problems be convergent is given.
Lucas Jódar, J. L. Morera, E. Navarro
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1973
The structure of general m-stage k-step methods in the sense of Def. 2.1.8 and 2.1.10 is so complex that we will deal in this chapter only with the special class of one-stage k-step methods whose forward-step procedures consist simply of a linear combination of values of η μ and f (η μ ) at k + 1 consecutive gridpoints t µ , μ= v −k(1)v.
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The structure of general m-stage k-step methods in the sense of Def. 2.1.8 and 2.1.10 is so complex that we will deal in this chapter only with the special class of one-stage k-step methods whose forward-step procedures consist simply of a linear combination of values of η μ and f (η μ ) at k + 1 consecutive gridpoints t µ , μ= v −k(1)v.
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