A Chebyshev multidomain adaptive mesh method for reaction-diffusion equations

Reaction-diffusion equations can present solutions in the form of traveling waves with stiff wave fronts. Such evolve different spatial and temporal scales, it is desired to construct numerical methods that adopt refinement at locations where solution becomes stiff. In this work, we develop a high-order adaptive mesh method based on Chebyshev spectral multidomain approach for reaction-diffusion equations. The proposed uses non-conforming non-overlapping adaptation computational mesh. have been used solving PDEs including However, non-conformal, not community. solves given each subdomain locally first boundary interface conditions are enforced global manner. way, be parallelizable efficient large systems. We show stable accurate solutions. provide both one- two-dimensional results efficacy method. application equations, yield solutions, new needs further investigation.