Solution Interpolation Method for Highly Oscillating Hyperbolic Equations
This paper deals with a novel numerical scheme for hyperbolic equations with rapidly changing terms. We are especially interested in the quasilinear equation ut+aux=f(x)u+g(x)un and the wave equation utt=f(x)uxx that have a highly oscillating term like f(x)=sin(x/ε), ε≪1. It also applies to the eq...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/546031 |
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| _version_ | 1832566810234322944 |
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| author | Pilwon Kim Chang Hyeong Lee |
| author_facet | Pilwon Kim Chang Hyeong Lee |
| author_sort | Pilwon Kim |
| collection | DOAJ |
| description | This paper deals with a novel numerical scheme for hyperbolic equations with
rapidly changing terms. We are especially interested in the quasilinear equation ut+aux=f(x)u+g(x)un and the wave equation utt=f(x)uxx that have a highly
oscillating term like f(x)=sin(x/ε), ε≪1. It also applies to the equations involving rapidly changing or even discontinuous coefficients. The method is based on the
solution interpolation and the underlying idea is to establish a numerical scheme by
interpolating numerical data with a parameterized solution of the equation. While the
constructed numerical schemes retain the same stability condition, they carry both
quantitatively and qualitatively better performances than the standard method. |
| format | Article |
| id | doaj-art-3ae961d86ed542baa55bae26ee7930d4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-3ae961d86ed542baa55bae26ee7930d42025-02-03T01:03:00ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/546031546031Solution Interpolation Method for Highly Oscillating Hyperbolic EquationsPilwon Kim0Chang Hyeong Lee1Ulsan National Institute of Science and Technology (UNIST), Ulsan Metropolitan City 689-798, Republic of KoreaUlsan National Institute of Science and Technology (UNIST), Ulsan Metropolitan City 689-798, Republic of KoreaThis paper deals with a novel numerical scheme for hyperbolic equations with rapidly changing terms. We are especially interested in the quasilinear equation ut+aux=f(x)u+g(x)un and the wave equation utt=f(x)uxx that have a highly oscillating term like f(x)=sin(x/ε), ε≪1. It also applies to the equations involving rapidly changing or even discontinuous coefficients. The method is based on the solution interpolation and the underlying idea is to establish a numerical scheme by interpolating numerical data with a parameterized solution of the equation. While the constructed numerical schemes retain the same stability condition, they carry both quantitatively and qualitatively better performances than the standard method.http://dx.doi.org/10.1155/2013/546031 |
| spellingShingle | Pilwon Kim Chang Hyeong Lee Solution Interpolation Method for Highly Oscillating Hyperbolic Equations Journal of Applied Mathematics |
| title | Solution Interpolation Method for Highly Oscillating Hyperbolic Equations |
| title_full | Solution Interpolation Method for Highly Oscillating Hyperbolic Equations |
| title_fullStr | Solution Interpolation Method for Highly Oscillating Hyperbolic Equations |
| title_full_unstemmed | Solution Interpolation Method for Highly Oscillating Hyperbolic Equations |
| title_short | Solution Interpolation Method for Highly Oscillating Hyperbolic Equations |
| title_sort | solution interpolation method for highly oscillating hyperbolic equations |
| url | http://dx.doi.org/10.1155/2013/546031 |
| work_keys_str_mv | AT pilwonkim solutioninterpolationmethodforhighlyoscillatinghyperbolicequations AT changhyeonglee solutioninterpolationmethodforhighlyoscillatinghyperbolicequations |