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Collocation Methods for Volterra Integral and Integro-Differential Equations: A Review
Axioms, 2018 We present a collection of recent results on the numerical approximation of Volterra integral equations and integro-differential equations by means of collocation type methods, which are able to provide better balances between accuracy and stability ...
Angelamaria Cardone +3 more
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Global error estimation of linear multistep methods through the Runge-Kutta methods [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2016 In this paper, we study the global truncation error of the linear multistep methods (LMM) in terms of local truncation error of the corresponding Runge-Kutta schemes. The key idea is the representation of LMM with a corresponding Runge-Kutta method.
Javad Farzi
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Multistep Lattice Boltzmann Methods: Theory and Applications
, 2022 S.156-169This paper presents a framework for incorporating arbitrary implicit multistep schemes into the lattice Boltzmann method. While the temporal discretization of the lattice Boltzmann equation is usually derived using a second-order trapezoidal ...
Wilde, Dominik +4 more
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Numerical Integration Schemes Based on Composition of Adjoint Multistep Methods
Algorithms, 2022 A composition is a powerful tool for obtaining new numerical methods for solving differential equations. Composition ODE solvers are usually based on single-step basic methods applied with a certain set of step coefficients.
Dmitriy Pesterev +4 more
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Известия Иркутского государственного университета: Серия "Математика", 2017 In the paper, we consider interrelated algebraic equations and Volterra linear integral equations of the first and second kind with variable limits of integration, where the lower limit of integration is strictly less than the upper limit for any values ...
M.N. Botoroeva, M. V. Bulatov
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, 2022 *** DOWNLOAD THE LATEST VERSION FROM GITHUB *** https://github.com/SalimGoudarzi/Generalised-Multistep-Dynamic ...
Salim Goudarzi
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Blended Linear Multistep Methods
ACM Transactions on Mathematical Software, 1977 The accuracy of linear multistep formulas suitable for stiff differential systems is limited. Greater accuracy can be attained by including higher derivatives in the formula, but this is not practical for all problems. It is possible however, to duplicate the absolute stability region for any given m-derivative multistep formula by taking a combination
Skeel, Robert D., Kong, Antony K.
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Numerical Stability and Performance of Semi-Explicit and Semi-Implicit Predictor–Corrector Methods
Mathematics, 2022 Semi-implicit multistep methods are an efficient tool for solving large-scale ODE systems. This recently emerged technique is based on modified Adams–Bashforth–Moulton (ABM) methods.
Loïc Beuken +4 more
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An algorithm for starting multistep methods
Computers & Mathematics with Applications, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tirani, R., Paracelli, C.
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Linear Multistep Methods for Impulsive Differential Equations
Discrete Dynamics in Nature and Society, 2012 This paper deals with the convergence and stability of linear multistep methods for impulsive differential equations. Numerical experiments demonstrate that both the mid-point rule and two-step BDF method are of order p=0 when applied to impulsive ...
X. Liu, M. H. Song, M. Z. Liu
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