- 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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