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

Document Type : Research Article

Authors

• Feyisa Edosa Merga
• Gemechis File Duressa

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 $t=0$.

Keywords

• Singularly Perturbed
• Quasilinear
• Sobolev Trigonometric B-spline

Main Subjects

• Numerical Analysis

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