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Numerical solution of non-planar Burgers equation by Haar wavelet method | ||
| Journal of Mathematical Modeling | ||
| مقاله 2، دوره 5، شماره 2، اسفند 2017، صفحه 89-118 اصل مقاله (1.01 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2017.2460 | ||
| نویسندگان | ||
| Sumana R Shesha* 1؛ Achala L. Nargund2؛ Nagendrappa M. Bujurke2 | ||
| 1Bangalore University | ||
| 2Department of Studies in Mathematics, Karnatak University, Dharwad, India | ||
| چکیده | ||
| In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a finite number of variables. The solution obtained by Haar wavelet collocation method is compared with that obtained by finite difference method and are found to be in good agreement. Shock waves are found to be formed due to nonlinearity and dissipation. We have analyzed the effects of non-planar and nonlinear geometry on shock existence. We observe that non-planar shock structures are different from planar ones. It is of interest to find that Haar wavelets enable to predict the shock structure accurately. | ||
| کلیدواژه‌ها | ||
| Haar wavelets؛ non-planar Burgers equation؛ quasilinearization؛ collocation points؛ finite difference؛ cylindrical and spherical geometry | ||
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آمار تعداد مشاهده مقاله: 1,134 تعداد دریافت فایل اصل مقاله: 1,271 |
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