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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Mean-square contractivity of stochastic $\theta$-methods [PDF]
, 2020 The paper is focused on the nonlinear stability analysis of stochastic $\theta$-methods. In particular, we consider nonlinear stochastic differential equations such that the mean-square deviation between two solutions exponentially decays, i.e., a mean ...
D'Ambrosio, Raffaele +1 more
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Numerical periodic normalization for codim 2 bifurcations of limit cycles : computational formulas, numerical implementation, and examples [PDF]
, 2013 Explicit computational formulas for the coefficients of the periodic normal forms for codimension 2 (codim 2) bifurcations of limit cycles in generic autonomous ODEs are derived.
De Witte, Virginie +3 more
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Delay-dependent stability of linear multi-step methods for linear neutral systems [PDF]
, 2020 summary:In this paper, we are concerned with numerical methods for linear neutral systems with multiple delays. For delay-dependently stable neutral systems, we ask what conditions must be imposed on linear multi-step methods in order that the numerical ...
Hu, Guang-Da, Shao, Lizhen
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The Essential Stability of Local Error Control for Dynamical Systems [PDF]
, 1995 Although most adaptive software for initial value problems is designed with an accuracy requirement—control of the local error—it is frequently observed that stability is imparted by the adaptation.
Humphries, A. R., Stuart, A. M.
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Equations with infinite delay : Numerical bifurcation analysis via pseudospectral discretization [PDF]
, 2018 We address the problem of the numerical bifurcation analysis of general nonlinear delay equations, including integral and integro-differential equations, for which no software is currently available.
Gyllenberg, Mats +2 more
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Computing the eigenvalues of realistic Daphnia models by pseudospectral methods [PDF]
, 2015 This work deals with physiologically structured populations of the Daphnia type. Their biological modeling poses several computational challenges. In such models, indeed, the evolution of a size structured consumer described by a Volterra functional ...
Breda, Dimitri +3 more
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On the numerical structure preservation of nonlinear damped stochastic oscillators [PDF]
, 2020 The paper is focused on analyzing the conservation issues of stochastic-methods when applied to nonlinear damped stochastic oscillators. In particular, we are interested in reproducing the long-term properties of the continuous problem over its ...
D'Ambrosio R., Scalone C.
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An asynchronous leapfrog method II [PDF]
, 2016 A second order explicit one-step numerical method for the initial value problem of the general ordinary differential equation is proposed. It is obtained by natural modifications of the well-known leapfrog method, which is a second order, two-step ...
Mutze, Ulrich
core
The Asymptotic Iteration Method Revisited
, 2020 The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical physics. The analysis
Ismail, Mourad E. H., Saad, Nasser
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