Nonpolynomial B-spline collocation method for solving singularly perturbed quasilinear Sobolev equation

Iranian Journal of Numerical Analysis and Optimization

مقاله 1، دوره 14، Issue 3 - شماره پیاپی 30، آذر 2024، صفحه 638-661   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.85929.1363

نویسندگان

F. Edosa Merga^* ؛ G. File Duressa

Department of Mathematics, Jimma University, Jimma, Oromia, Ethiopia.

چکیده

In this paper, a singularly perturbed one-dimensional initial boundary value problem of a quasilinear Sobolev-type equation is presented. The nonlinear term of the problem is linearized by Newton’s linearization method. Time derivatives are discretized by implicit Euler’s method on nonuniform step size. A uniform trigonometric B-spline collocation method is used to treat the spatial variable. The convergence analysis of the scheme is proved, and the accuracy of the method is of order two in space and order one in time direction, respectively. To test the efficiency of the method, a model example is demonstrated. Results of the scheme are presented in tabular, and the figure indicates the scheme is uniformly convergent and has an initial layer at t = 0.

کلیدواژه‌ها

Singularly perturbed؛ Quasilinear؛ Sobolev؛ Trigonometric B-spline

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