TY - JOUR T1 - Highly Oscillatory Diffusion-Type Equations JO - Journal of Computational Mathematics VL - 6 SP - 549 EP - 572 PY - 2013 DA - 2013/12 SN - 31 DO - http://doi.org/10.4208/jcm.1307-m3955 UR - https://global-sci.org/intro/article_detail/jcm/9754.html KW - Diffusion-type PDEs, High oscillation, Asymptotic expansions, Modulated Fourier expansions. AB -

We explore new asymptotic-numeric solvers for partial differential equations with highly oscillatory forcing terms. Such methods represent the solution as an asymptotic series, whose terms can be evaluated by solving non-oscillatory problems and they guarantee high accuracy at a low computational cost. We consider two forms of oscillatory forcing terms, namely when the oscillation is in time or in space: each lends itself to different treatment. Numerical examples highlight the salient features of the new approach.