Numerical Treatment of Singular BVPs: The New MATLAB Code bvpsuite

Kitzhofer, G.; Koch, Othmar; Weinmüller, Ewa

doi:10.1063/1.3241480

Cited by 7 publications

(4 citation statements)

References 27 publications

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“…To numerically solve the resulting equations the bvpsuite1.1 software package was used . The results of calculations coincide with the results of the paper and with those in the paper .…”

Section: Theoretical Basissupporting

confidence: 77%

Morphology of Ionic Micelles as Studied by Numerical Solution of the Poisson Equation

2022

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“…To numerically solve the resulting equations the bvpsuite1.1 software package was used . The results of calculations coincide with the results of the paper and with those in the paper .…”

Section: Theoretical Basissupporting

confidence: 77%

Morphology of Ionic Micelles as Studied by Numerical Solution of the Poisson Equation

2022

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“…To solve this EVP, we employ a MATLAB boundary-value-problem solver BVPSuite in its eigen-value mode (see Kitzhofer et al 2009, for a detailed description of the code). In the appendix to Li et al (2014), we have performed an extensive validation study of this code using available analytical solutions in the context of coronal seismology.…”

Section: Governing Equations and Methods Of Solutionmentioning

confidence: 99%

Impulsively Generated Wave Trains in Coronal Structures. I. Effects of Transverse Structuring on Sausage Waves in Pressureless Tubes

Chen

et al. 2017

ApJ

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The behavior of the axial group speeds of trapped sausage modes plays an important role in determining impulsively generated wave trains, which have often been invoked to account for quasi-periodic signals with quasi-periods of order seconds in a considerable number of coronal structures. We conduct a comprehensive eigenmode analysis, both analytically and numerically, on the dispersive properties of sausage modes in pressureless tubes with three families of continuous radial density profiles. We find a rich variety of the dependence on the axial wavenumber k of the axial group speed v gr . Depending on the density contrast and profile steepness as well as on the detailed profile description, the v gr − k curves either possess or do not possess cutoff wavenumbers, and they can behave in either a monotonical or non-monotonical manner. With time-dependent simulations, we further show that this rich variety of the group speed characteristics heavily influences the temporal evolution and Morlet spectra of impulsively -2 -generated wave trains. In particular, the Morlet spectra can look substantially different from "crazy tadpoles" found for the much-studied discontinuous density profiles. We conclude that it is necessary to re-examine available high-cadence data to look for the rich set of temporal and spectral features, which can be employed to discriminate between the unknown forms of the density distributions transverse to coronal structures.

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“…In particular, algebraic constraints are permitted and therefore, DAEs are in the scope of the code. In [24,26] numerical experiments and comparisons with existing software can be found. We stress that in the present paper, we only use bvpsuite executed on uniform grids in order to illustrate the convergence order of the involved collocation schemes.…”

Section: Introductionmentioning

confidence: 99%

Convergence of collocation schemes for boundary value problems in nonlinear index 1 DAEs with a singular point

Dick¹,

Koch²,

März³

et al. 2012

Math. Comp.

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We analyze the convergence behavior of collocation schemes applied to approximate solutions of BVPs in nonlinear index 1 DAEs, which exhibit a critical point at the left boundary. Such a critical point of the DAE causes a singularity in the inherent nonlinear ODE system. In particular, we focus on the case when the inherent ODE system is singular with a singularity of the first kind and apply polynomial collocation to the original DAE system. We show that for a certain class of well-posed boundary value problems in DAEs having a sufficiently smooth solution, the global error of the collocation scheme converges uniformly with the so-called stage order. Due to the singularity, superconvergence at the mesh points does not hold in general. The theoretical results are supported by numerical experiments.

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Numerical Treatment of Singular BVPs: The New MATLAB Code bvpsuite

Cited by 7 publications

References 27 publications

Morphology of Ionic Micelles as Studied by Numerical Solution of the Poisson Equation

Morphology of Ionic Micelles as Studied by Numerical Solution of the Poisson Equation

Impulsively Generated Wave Trains in Coronal Structures. I. Effects of Transverse Structuring on Sausage Waves in Pressureless Tubes

Convergence of collocation schemes for boundary value problems in nonlinear index 1 DAEs with a singular point

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