Results 231 to 240 of about 64,667 (273)
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Improved multistep method with non‐linear corrections
International Journal for Numerical Methods in Biomedical Engineering, 2008AbstractA new semi‐implicit class of multistep methods for stiff ordinary differential equations is presented. The general method is based on the application of estimation functions not only for the derivatives but also for the state variables. This permits the transformation of the original system in a purely algebraic system using the solutions of ...
Boroni, G., Lotito, P., Clausse, A.
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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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Multiplier and contractivity methods for linear multistep methods
Applied Numerical Mathematics, 1989zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Odeh, F., Nevanlinna, O., Liniger, W.
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DYNAMICS OF LINEAR MULTISTEP METHODS FOR DELAY DIFFERENTIAL EQUATIONS
International Journal of Bifurcation and Chaos, 2004In this paper we study the relationship between the asymptotic behavior of a numerical simulation by linear multistep method and that of the true solution itself for fixed step sizes. The numerical method is viewed as a dynamical system in which the step size acts as a parameter.
Hongjiong Tian, Qian Guo 0002
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Nonautonomous stability of linear multistep methods
IMA Journal of Numerical Analysis, 2009A linear scalar nonautonomous initial-value problem (IVP) is governed by a scalar lambda(t) with a nonpositive real part. For a wide class of linear multistep methods, including BDF4-6, it is shown that negative real lambda(t) may be chosen to generate instability in the method when applied to the IVP.
B. R. Boutelje, A. T. Hill
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On Stiffly Stable Implicit Linear Multistep Methods
SIAM Journal on Numerical Analysis, 1972Sufficient conditions for a consistent linear multistep method to be stiffly stable are given. These conditions involve properties of the stability mapping from the extended complex plane onto itself.
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On the convergence of advanced linear multistep methods
BIT, 1979A convergence theorem is given showing that zero-stable advanced linear multistep methods with orderp consistency have orderp convergence.
McKee, S., Pitcher, N.
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Multiplier techniques for linear multistep methods
Numerical Functional Analysis and Optimization, 1981A theory is developed for the fixed-h stability of integration schemes based on A(α)-stable formulas when applied to nonlinear parabolic-like stiff equations. The theory is based on a general multiplier technique whose properties we fully develop.
Olavi Nevanlinna, F. Odeh
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Factored, a-stable, linear multistep methods
ACM SIGNUM Newsletter, 1979Historically, the development and analysis of methods for ordinary differential equations (ODEs) have been more advanced than those for partial differential equations (PDEs). The present state of numerical methods is no exception; therefore, it behooves the numerical analyst to exploit sophisticated ODE methods for the numerical solution of PDEs.
R. F. Warming, Richard M. Beam
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A Generalization of Linear Multistep Methods
1990A generalization of the methods that are currently available to solve systems of ordinary differential equations is made. This generalization is made by constructing linear multistep methods from an arbitrary set of monotone interpolating and approximating functions. Local truncation error estimates as well as stability analysis is given. Specifically,
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