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An in-depth numerical study of the two-dimensional Kuramoto–Sivashinsky equation (2015)
Journal Article
Kalogirou, A., Keaveny, E. E., & Papageorgiou, D. T. (2015). An in-depth numerical study of the two-dimensional Kuramoto–Sivashinsky equation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2179), Article 20140932. https://doi.org/10.1098/rspa.2014.0932

The Kuramoto–Sivashinsky equation in one spatial dimension (1D KSE) is one of the most well-known and well-studied partial differential equations. It exhibits spatio-temporal chaos that emerges through various bifurcations as the domain length increa... Read More about An in-depth numerical study of the two-dimensional Kuramoto–Sivashinsky equation.

Linearly implicit schemes for multi-dimensional Kuramoto–Sivashinsky type equations arising in falling film flows (2015)
Journal Article
Akrivis, G., Kalogirou, A., Papageorgiou, D. T., & Smyrlis, Y. (2016). Linearly implicit schemes for multi-dimensional Kuramoto–Sivashinsky type equations arising in falling film flows. IMA Journal of Numerical Analysis, 36(1), 317–336. https://doi.org/10.1093/imanum/drv011

This study introduces, analyses and implements space-time discretizations of two-dimensional active dissipative partial differential equations such as the Topper–Kawahara equation; this is the two-dimensional extension of the dispersively modified Ku... Read More about Linearly implicit schemes for multi-dimensional Kuramoto–Sivashinsky type equations arising in falling film flows.