Results 241 to 250 of about 12,007,006 (285)
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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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1973
Having studied the peculiarities of multistage and multistep methods separately in Chapters 3 and 4 by analyzing their simplest representative classes we will now consider discretization methods for IVP1 which combine the features of multistage and multisteps methods, cf. Section 2.1.3. We will, however, still restrict ourselves to forward step methods
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Having studied the peculiarities of multistage and multistep methods separately in Chapters 3 and 4 by analyzing their simplest representative classes we will now consider discretization methods for IVP1 which combine the features of multistage and multisteps methods, cf. Section 2.1.3. We will, however, still restrict ourselves to forward step methods
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Multistep methods on manifolds
IMA Journal of Numerical Analysis, 2001The author discusses the preservation of invariants of an ordinary differential equation in a numerical integration. He considers methods of Taylor type, i.e. methods of order \(p\) where the leading term in the error analysis is given by the \((p+1)\)th derivative of the solution.
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Multistep methods for differential algebraic equations
Numerical Algorithms, 1995Multistep methods for specially structured implicit nonlinear differential algebraic equations under index 1 conditions are considered. The existence and uniqueness of a numerical solution is shown. There is no discussion about the progress of this paper in comparison to previous ones, e.g. \textit{E. Griepentrog} and \textit{R.
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