Mesh selection strategies of the code TOM for Boundary Value Problems

Mazzia, Francesca

doi:10.1007/s11565-022-00440-7

Cited by 3 publications

(2 citation statements)

References 35 publications

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“…We use different values of the parameter λ and we select input tolerances atol = rtol as 10 −3 , 10 −4 , • • • , 10 −8 . The code TOM is used with the BS method of order 6 and the hybrid mesh selection denoted NSSE [Mazzia, 2022], designed for the solution of non stiff problems. The work precision diagrams are reported in Figures 5-6.…”

Section: Numerical Solution Of Boundary Value Problemsmentioning

confidence: 99%

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The Object Oriented c++ library QIBSH++ for Hermite spline Quasi Interpolation

Bertolazzi¹,

Falini²,

Mazzia³

2022

Preprint

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The library QIBSH++ is a C++ object oriented library for the solution of Quasi Interpolation problems. The library is based on a Hermite Quasi Interpolating operator, which was derived as continuous extensions of linear multistep methods applied for the numerical solution of Boundary Value Problems for Ordinary Differential Equations. The library includes the possibility to use Hermite data or to apply a finite difference scheme for derivative approximations, when derivative values are not directly available. The generalization of the quasi interpolation procedure to surfaces and volumes approximation by means of a tensor product technique is also implemented. The method has been also generalized for one dimensional vectorial data, periodic data, and for two dimensional data in cylindrical coordinates, periodic with respect to the angular argument. Numerical tests show that the library could be used efficiently in many practical problems.

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Section: Numerical Solution Of Boundary Value Problemsmentioning

confidence: 99%

“…In this case Figure 6 clearly show the efficiency of the code TOM QIBSH++. Further experiments using the code can been found in [Mazzia and Settanni, 2021;Mazzia, 2022].…”

Section: Numerical Solution Of Boundary Value Problemsmentioning

confidence: 99%

The Object Oriented c++ library QIBSH++ for Hermite spline Quasi Interpolation

Bertolazzi¹,

Falini²,

Mazzia³

2022

Preprint

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Hermite–Birkhoff spline Quasi-Interpolation with application as dense output for Gauss–Legendre and Gauss–Lobatto Runge–Kutta schemes

Falini

Mazzia

Sestini

2024

Applied Numerical Mathematics

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Fluid statics of a self-gravitating isothermal sphere of van der Waals' gas

Giordano,

Amodio,

Iavernaro

et al. 2024

Physics of Fluids

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We subject to scrutiny the physical consistency of adopting the perfect-gas thermodynamic model within self-gravitation circumstances by studying the fluid statics of a self-gravitating isothermal sphere with the van der Waals' thermodynamic model, whose equation of state features well-known terms that account for molecular attraction and size. The governing equations are formulated for any thermodynamic model with two intensive degrees of freedom, applied with the van der Waals' model and solved numerically in nondimensional form by finite-difference algorithms. After a brief summary of thermodynamic characteristics possessed by the van der Waals' model, and relevant to the present study, we proceed to the description of the results in terms of comparative graphs illustrating radial profiles of density, pressure, and gravitational field. We complement them with graphs that compare the dependence of central and wall densities on gravitational number for both perfect-gas and van der Waals' models and that attest dramatically and unequivocally how the presence of molecular-attraction and -size terms removes questionable fluid-statics results systematically found accompanying the perfect-gas model in standard treatments. We also describe, within a very brief and preliminary digression, how the sanitizing action of the mentioned terms affects the thermodynamics of the isothermal sphere by providing evidence of how the gravitational correction to entropy corresponding to the van der Waals' model makes sure that there is no risk of gravothermal catastrophes, negative specific heats, and thermal instabilities. Furthermore, we investigate the phenomenology related to self-gravitationally induced both liquid-gas phase equilibria and metastable-gas states and we describe how they arise naturally and self-consistently from the governing equations. We conclude with a summary of the main results and with a challenging proposal of future work meant to attempt a revalorization the perfect-gas model.

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Mesh selection strategies of the code TOM for Boundary Value Problems

Cited by 3 publications

References 35 publications

The Object Oriented c++ library QIBSH++ for Hermite spline Quasi Interpolation

The Object Oriented c++ library QIBSH++ for Hermite spline Quasi Interpolation

Hermite–Birkhoff spline Quasi-Interpolation with application as dense output for Gauss–Legendre and Gauss–Lobatto Runge–Kutta schemes

Fluid statics of a self-gravitating isothermal sphere of van der Waals' gas

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