Stability analysis of linear multistep methods for delay differential equations
International Journal of Mathematics and Mathematical Sciences, 1986 Stability properties of linear multistep methods for delay differential equations with respect to the test equation y′(t)=ay(λt)+by(t), t≥0 ...
V. L. Bakke, Z. Jackiewicz
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Unconditional Stability for Multistep ImEx Schemes: Theory [PDF]
, 2017 This paper presents a new class of high order linear ImEx multistep schemes with large regions of unconditional stability. Unconditional stability is a desirable property of a time stepping scheme, as it allows the choice of time step solely based on ...
Rosales, Rodolfo Ruben +3 more
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Adaptive Stepsize Control for Extrapolation Semi-Implicit Multistep ODE Solvers
Mathematics, 2021 Developing new and efficient numerical integration techniques is of great importance in applied mathematics and computer science. Among the variety of available methods, multistep ODE solvers are broadly used in simulation software.
Denis Butusov
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Numerical methods for solving nonlinear Volterra integro-differential equations based on Hermite–Birkhoff interpolation [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2020 We introduce a new family of multivalue and multistage methods based on Hermite–Birkhoff interpolation for solving nonlinear Volterra integro differential equations.
S. Fazeli
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Using Predictor-Corrector Methods for Numerical Solution of System of Non-linear Volterra Integral Equations of Second Kind [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2009 The aim of this paper is solving system of non-linear Volterra integral equations of the second kind (NSVIEK2) numerically using Predictor-Corrector methods (P-CM). Two multistep methods (Adams-Bashforth, Adams-Moulton).
Borhan Jumaa, Abbas Taqi
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Axioms, 2023 A computational approach with the aid of the Linear Multistep Method (LMM) for the numerical solution of differential equations with initial value problems or boundary conditions has appeared several times in the literature due to its good accuracy and ...
Ezekiel Olaoluwa Omole +4 more
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Multistep variable methods for exact integration of perturbed stiff linear systems [PDF]
, 2016 A family of real and analytical functions with values within the ring of M(m, R) is introduced. The solution for linear systems of differential equations is expressed as a series of Φ-functions.
Cortés-Molina, Mónica +2 more
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A-Stable High Order Hybrid Linear Multistep Methods for Stiff Problems
Journal of Algorithms & Computational Technology, 2014 This paper considers a new class of high order hybrid linear multistep methods for the numerical solution of stiff initial value problems (IVPs) in ordinary differential equations (ODEs).
R. I. Okuonghae
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Contractivity-preserving implicit linear multistep methods [PDF]
Mathematics of Computation, 1989 We investigate contractivity properties of implicit linear multistep methods in the numerical solution of ordinary differential equations. The emphasis is on nonlinear and linear systems d d t U ( t ) = f ( t , U (
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Uniform stability of linear multistep methods in Galerkin procedures for parabolic problems
International Journal of Mathematics and Mathematical Sciences, 1979 Linear multistep methods are considered which have a stability region S and are D-stable on the whole boundary ∂S⊂S of S. Error estimates are derived which hold uniformly for the class of initial value problems Y′=AY+B(t), t>0, Y(0)=Y0 with normal matrix
Eckart Gekeler
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