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Volume 31, Issue 6
Highly Oscillatory Diffusion-Type Equations

Sevda Üsküplü Altınbaşak, Marissa Condon, Alfredo Deaño & Arieh Iserles

DOI: 10.4208/jcm.1307-m3955

J. Comp. Math., 31 (2013), pp. 549-572.

Published online: 2013-12

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  • Abstract

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.

  • AMS Subject Headings

65M70, 35B05, 65M06, 35C20, 42A16.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-31-549, author = {Sevda Üsküplü Altınbaşak, Marissa Condon, Alfredo Deaño and Arieh Iserles}, title = {Highly Oscillatory Diffusion-Type Equations}, journal = {Journal of Computational Mathematics}, year = {2013}, volume = {31}, number = {6}, pages = {549--572}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1307-m3955}, url = {http://global-sci.org/intro/article_detail/jcm/9754.html} }
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 -

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.

Sevda Üsküplü Altınbaşak, Marissa Condon, Alfredo Deaño and Arieh Iserles. (2013). Highly Oscillatory Diffusion-Type Equations. Journal of Computational Mathematics. 31 (6). 549-572. doi:10.4208/jcm.1307-m3955
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