Can linear collocation ever beat quadratic?

Martin, R., Chappell, D.J. ORCID: 0000-0001-5819-0271, Chuzhanova, N. ORCID: 0000-0002-4655-3618 and Crofts, J.J. ORCID: 0000-0001-7751-9984, 2017. Can linear collocation ever beat quadratic? In: D.J. Chappell ORCID: 0000-0001-5819-0271, ed., Proceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), 10-11 July 2017, Nottingham Conference Centre, Nottingham Trent University. Nottingham: Nottingham Trent University: Publications, pp. 117-124. ISBN 9780993111297

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Computational approaches are becoming increasingly important in neuroscience, where complex, nonlinear systems modelling neural activity across multiple spatial and temporal scales are the norm. This paper considers collocation techniques for solving neural field models, which typically take the form of a partial integro-dfferential equation. In particular, we investigate and compare the convergence properties of linear and quadratic collocation on both regular grids and more general meshes not fixed to the regular Cartesian grid points. For regular grids we perform a comparative analysis against more standard techniques, in which the convolution integral is computed either by using Fourier based methods or via the trapezoidal rule. Perhaps surprisingly, we find that on regular, periodic meshes, linear collocation displays better convergence properties than quadratic collocation, and is in fact comparable with the spectral convergence displayed by both the Fourier based and trapezoidal techniques. However, for more general meshes we obtain superior convergence of the
convolution integral using higher order methods, as expected.

Item Type: Chapter in book
Description: Chapter 14.
Creators: Martin, R., Chappell, D.J., Chuzhanova, N. and Crofts, J.J.
Publisher: Nottingham Trent University: Publications
Place of Publication: Nottingham
Date: 2017
ISBN: 9780993111297
Rights: Copyright © 2017 The Authors.
Divisions: Schools > School of Science and Technology
Record created by: Jill Tomkinson
Date Added: 24 Aug 2017 11:38
Last Modified: 24 Aug 2017 12:46

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