TY - JOUR
T1 - Highly Oscillatory Diffusion-Type Equations
AU - Sevda Üsküplü Altınbaşak, Marissa Condon, Alfredo Deaño & Arieh Iserles
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 - <p style="text-align: justify;">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.</p>