An adaptive numerical scheme for a partial integro-differential equation

Title: An adaptive numerical scheme for a partial integro-differential equation
Creator: Georgiou, F.; Lamichhane, B. P.; Thamwattana, N.
Relation: ANZIAM Journal Vol. 60, Issue (CTAC2018), p. C187-C200
Publisher Link: http://dx.doi.org/10.21914/anziamj.v60i0.14066
Publisher: Australian Mathematical Publishing Association
Resource Type: journal article
Date: 2019
Description: One method of modelling cell-cell adhesion gives rise to a partial integro-differential equation. While non-adaptive techniques work in the numerical modelling of such an equation, there are also many opportunities for optimisation. The studied partial integro-differential equation has a tendency to produce aggregations leaving large regions where both the function value and derivative are equal to zero, leading to a higher resolution than needed and lower than desired resolution where the aggregations form. In order to overcome this we develop an adaptive scheme in both space and time using a modified form of Matlab's ode45 and finite volume methods to more efficiently simulate the studied partial integro-differential equation. We use our numerical scheme to simulate the problem presented by Armstrong et al.
Subject: partial integro-differential; equation; numerial; adaptive
Identifier: http://hdl.handle.net/1959.13/1477214
Identifier: uon:49940
Identifier: ISSN:1445-8810
Language: eng
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