Highly Oscillatory Diffusion-Type Equations (Journal of Computational Mathematics, 2021)
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.
Keywords: Diffusion-type PDEs; High oscillation; Asymptotic expansions; Modulated Fourier expansions.