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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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Error Estimate for a Linear Multistep Method
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1991For the system \(x=Tx+b\) of linear equations in a Banach space with \(T=T_ 0+...+T_ n\), \(n\geq 1\), we consider the implicit stationary n- step method \(x_{k+n}=\sum^{n}_{i=0}T_ ix_{k+n-i}+b,\) \(k=0,1,2,...\). In case of \(\| T\|
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Exact multistep distorted-wave method
Physical Review C, 1988We show that the coupled channel equations are exactly transformed into the T matrix of the multistep process. The consistency with empirical models is discussed.
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Stability Domains of Explicit Multistep Methods
Numerical Analysis and Applications, 2022Kireev, I. V. +2 more
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