Functionally Fitted Explicit Two Step Peer Methods

Montijano, J. I.; Rández, L.; Daele, Maarten Van; Calvo, M.

doi:10.1007/s10915-014-9951-9

Cited by 5 publications

(1 citation statement)

References 17 publications

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“…Exponential fitting is a mathematical procedure to generate numerical methods for different problems with a pronounced oscillatory or hyperbolic behaviour, usually occurring in interpolation, numerical differentiation and quadrature [ 30 , 31 , 33 , 35 , 60 , 64 , 65 , 70 , 78 ], numerical solution of first order ordinary differential equations [ 3 , 4 , 27 , 40 , 43 , 49 , 60 , 68 , 72 , 73 , 75 , 76 , 79 ], second order differential equations [ 54 , 63 ], integral equations [ 15 , 16 ], fractional differential equations [ 1 ], partial differential equations [ 14 , 45 , 46 , 50 , 52 ]. This procedure has been introduced in [ 62 ].…”

Section: Introductionmentioning

confidence: 99%

User-Friendly Expressions of the Coefficients of Some Exponentially Fitted Methods

Conte

D’Ambrosio

Giordano

et al. 2020

Computational Science and Its Applications – ICCSA 2020

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The purpose of this work consists in reformulating the coefficients of some exponentially-fitted (EF) methods with the aim of avoiding numerical cancellations and loss of precision. Usually the coefficients of an EF method are expressed in terms of , where is the frequency and h is the step size. Often, these coefficients exhibit a 0/0 indeterminate form when . To avoid this feature we will use two sets of functions, called C and S , which have been introduced by Ixaru in [ 61 ]. We show that the reformulation of the coefficients in terms of these functions leads to a complete removal of the indeterminacy and thus the convergence of the corresponding EF method is restored. Numerical results will be shown to highlight these properties.

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Section: Introductionmentioning

confidence: 99%

User-Friendly Expressions of the Coefficients of Some Exponentially Fitted Methods

Conte

D’Ambrosio

Giordano

et al. 2020

Computational Science and Its Applications – ICCSA 2020

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Jacobian-Dependent Two-Stage Peer Method for Ordinary Differential Equations

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Pagano

Paternoster

2021

Computational Science and Its Applications – ICCSA 2021

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Analysis of spectral Hamiltonian boundary value methods (SHBVMs) for the numerical solution of ODE problems

2019

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Recently, the numerical solution of stiffly/highly-oscillatory Hamiltonian problems has been attacked by using Hamiltonian Boundary Value Methods (HBVMs) as spectral methods in time. While a theoretical analysis of this spectral approach has been only partially addressed, there is enough numerical evidence that it turns out to be very effective even when applied to a wider range of problems. Here we fill this gap by providing a thorough convergence analysis of the methods and confirm the theoretical results with the aid of a few numerical tests.

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Functionally Fitted Explicit Two Step Peer Methods

Cited by 5 publications

References 17 publications

User-Friendly Expressions of the Coefficients of Some Exponentially Fitted Methods

User-Friendly Expressions of the Coefficients of Some Exponentially Fitted Methods

Jacobian-Dependent Two-Stage Peer Method for Ordinary Differential Equations

Analysis of spectral Hamiltonian boundary value methods (SHBVMs) for the numerical solution of ODE problems

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