AbstractA Chebyshev collocation method is proposed for the computation of laminar flame propagation in a two‐dimensional gaseous medium. The method is based on a domain decomposition technique associated with co‐ordinate transforms to map the infinite physical subdomains into finite computational ones. The influence matrix method is used to handle the patching conditions at the interfaces. This technique is particularly efficient since at each time step only matrix products have to be performed. The method is tested first on an elliptic model problem; it is then applied to laminar flame computations, including calculations of cellular instabilities of flame fro