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Wondimu, Getu, Duressa, Gemechis File, Woldaregay, Mesfin, Dinka, Tekle. (1402). A uniformly convergent computational method for singularly perturbed parabolic partial differential equation with integral boundary condition. فیزیولوژی و بیوتکنولوژی آبزیان, 12(1), 157-175. doi: 10.22124/jmm.2023.24590.2198
Getu Mekonnen Wondimu; Gemechis File Duressa; Mesfin Mekuria Woldaregay; Tekle Gemechu Dinka. "A uniformly convergent computational method for singularly perturbed parabolic partial differential equation with integral boundary condition". فیزیولوژی و بیوتکنولوژی آبزیان, 12, 1, 1402, 157-175. doi: 10.22124/jmm.2023.24590.2198
Wondimu, Getu, Duressa, Gemechis File, Woldaregay, Mesfin, Dinka, Tekle. (1402). 'A uniformly convergent computational method for singularly perturbed parabolic partial differential equation with integral boundary condition', فیزیولوژی و بیوتکنولوژی آبزیان, 12(1), pp. 157-175. doi: 10.22124/jmm.2023.24590.2198
Wondimu, Getu, Duressa, Gemechis File, Woldaregay, Mesfin, Dinka, Tekle. A uniformly convergent computational method for singularly perturbed parabolic partial differential equation with integral boundary condition. فیزیولوژی و بیوتکنولوژی آبزیان, 1402; 12(1): 157-175. doi: 10.22124/jmm.2023.24590.2198

A uniformly convergent computational method for singularly perturbed parabolic partial differential equation with integral boundary condition

Journal of Mathematical Modeling
دوره 12، شماره 1، خرداد 2024، صفحه 157-175    اصل مقاله (492.75 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2023.24590.2198
نویسندگان
Getu Mekonnen Wondimu* 1؛ Gemechis File Duressa2؛ Mesfin Mekuria Woldaregay3؛ Tekle Gemechu Dinka4
1Mathematics Department, Adama Raya University, Maichew, Ethiopia
2Department of Mathematics, Jimma University, Jimma, Ethiopia
3Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia
4Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia
چکیده
This paper presents a numerical method for a class of singularly perturbed parabolic partial differential equations with integral boundary conditions (IBC). The solution to the considered problem exhibits pronounced boundary layers on both the left and right sides of the spatial domain. To address this challenging problem, we propose the use of the implicit Euler method for time discretization and a finite difference method on a well-designed piecewise uniform Shishkin mesh for spatial discretization. The integral boundary condition is approximated using Simpson's $\frac{1}{3}$ rule. The presented method demonstrates almost second-order uniform convergence in the discretization of the spatial derivative and first-order convergence in the discretization of the time derivative. To validate the applicability and accuracy of the proposed method, two illustrative examples are employed. The computational results not only accurately reflect the theoretical estimations but also highlight the method's effectiveness in capturing the intricate features of singularly perturbed parabolic partial differential equations with integral boundary conditions.
کلیدواژه‌ها
Singularly perturbed problems؛ finite difference؛ Shishkin mesh؛ uniform convergence؛ integral boundary condition
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تعداد مشاهده مقاله: 112
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