An analysis of the reliability of error control B-spline Gaussian collocation PDE software.

*(English)*Zbl 1355.65139
BĂ©lair, Jacques (ed.) et al., Mathematical and computational approaches in advancing modern science and engineering. Based on the international conference on applied mathematics, modeling and computational science, AMMCS, jointly held with the annual meeting of the Canadian applied and industrial mathematics, CAIMS, June 7–15, 2015. Cham: Springer (ISBN 978-3-319-30377-2/hbk; 978-3-319-30379-6/ebook). 459-468 (2016).

Summary: B-spline Gaussian collocation software for the numerical solution of PDEs has been widely used for several decades. BACOL and BACOLI are recently developed packages of this class that provide control of estimates of the temporal and spatial errors of the numerical solution through the use of adaptive time-stepping/adaptive time integration method order selection and adaptive spatial mesh refinement. Previous studies have investigated the performance of the BACOL and BACOLI packages, primarily with respect to work-accuracy measures. In this paper, we investigate the reliability of the BACOL and BACOLI packages, focusing on the relationship between the requested tolerance and the accuracy achieved. In particular, we consider the effect, on the reliability of the software, of (i) the degree of the piecewise polynomials employed in the representation of the spatial dependence of the approximate solution, (ii) the type of spatial error control employed, and (iii) the type of spatial error estimate computed.

For the entire collection see [Zbl 1362.00026].

For the entire collection see [Zbl 1362.00026].

##### MSC:

65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |

65D07 | Numerical computation using splines |

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\textit{P. Muir} and \textit{J. Pew}, in: Mathematical and computational approaches in advancing modern science and engineering. Based on the international conference on applied mathematics, modeling and computational science, AMMCS, jointly held with the annual meeting of the Canadian applied and industrial mathematics, CAIMS, June 7--15, 2015. Cham: Springer. 459--468 (2016; Zbl 1355.65139)

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