Bunder, J.Roberts, A.2012-07-022012-07-022012Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 2012, vol.53, iss.SUPPL, pp.280-2951446-87351446-8735http://hdl.handle.net/2440/71981Proceedings of the 10th Biennial Engineering Mathematics and Applications Conference (EMAC2011) held at University Technology Sydney in December 2011We discuss efficient macroscale modelling of microscale systems using patch dynamics. This pilot study effectively homogenises microscale varying diffusion in one dimension. The `equation free' approach requires that the microscale model be solved only on small spatial patches. Suitable boundary conditions ensure that these patches are well coupled. By centre manifold theory, an emergent closed model exists on the macroscale. Patch dynamics systematically approximates this macroscale model. The modelling is readily adaptable to higher dimensions and to reaction-diffusion equations.en© Austral. Mathematical Soc. 2012.multiscale modellingpatch dynamicscoupled boundary conditionsdifference equationsConference paper00300008542012062114345810.21914/anziamj.v53i0.507497 Expanding Knowledge9701 Expanding Knowledge970101 Expanding Knowledge in the Mathematical Sciences01 Mathematical Sciences0103 Numerical and Computational Mathematics010302 Numerical Solution of Differential and Integral Equations0004152487000182-s2.0-8489785060364860Bunder, J. [0000-0001-5355-2288]Roberts, A. [0000-0001-8930-1552]