Department of Mathematics, Jimma University, Jimma, Oromia, Ethiopia
10.22067/ijnao.2024.85929.1363
Abstract
In this paper, singularly perturbed one-dimensional initial boundary value problem of quasilinear Sobolev type equation is presented. The non-linear term of the problem is linearized by Newton's linearization method. Time derivatives is discretized by implicit Euler's method on non-uniform step size. A uniform trigonometric B-spline collocation method is used to treat the spatial variable. The convergence analysis of the scheme 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. The results of the scheme is presented in tabular and figure indicates the scheme is uniformly convergent and has initial layer at $t=0$.
Merga, F. E., & Duressa, G. F. (2024). Non-polynomial B-spline collocation method for solving singularly perturbed quasilinear Sobolev equation. Iranian Journal of Numerical Analysis and Optimization, (), -. doi: 10.22067/ijnao.2024.85929.1363
MLA
Feyisa Edosa Merga; Gemechis File Duressa. "Non-polynomial B-spline collocation method for solving singularly perturbed quasilinear Sobolev equation". Iranian Journal of Numerical Analysis and Optimization, , , 2024, -. doi: 10.22067/ijnao.2024.85929.1363
HARVARD
Merga, F. E., Duressa, G. F. (2024). 'Non-polynomial B-spline collocation method for solving singularly perturbed quasilinear Sobolev equation', Iranian Journal of Numerical Analysis and Optimization, (), pp. -. doi: 10.22067/ijnao.2024.85929.1363
VANCOUVER
Merga, F. E., Duressa, G. F. Non-polynomial B-spline collocation method for solving singularly perturbed quasilinear Sobolev equation. Iranian Journal of Numerical Analysis and Optimization, 2024; (): -. doi: 10.22067/ijnao.2024.85929.1363
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