Title: A new modified Taylor wavelets collocation method for solving convection diffusion and Benjamina Bona Mohany equations

Authors: Ankit Kumar; Sag Ram Verma

Addresses: Department of Mathematics, School of Allied Sciences, Mandsaur University, Mandsaur – 458001, Madhyapradesh, India ' Department of Mathematics and Statistics, Faculty of Science, Gurukula Kangri (Deemed to be University), Haridwar-249 404, India

Abstract: In this work, a novel method is presented for solving the convection-diffusion and Benjamina Bona Mohany equations. These partial differential equations are used for mathematical modelling of semiconductor and optical devices. The introduced method is based on new modified Taylor wavelets approximation which is directly used to convert the equations to a system of algebraic equation by combining collocation method. In this novel method, an improved factor is multiplied in the modified Taylor wavelets basis, which further improves the results. In addition, the effect of the improvement factor α and time on solution results of these problems for different domains of z is discussed in this paper. To demonstrate the reliability and stability of this novel method, we compared its results with previously used methods, such as the finite difference method, and Haar wavelet method. Consequently, the proposed method yields a significantly improved approximation solution for various classes of partial differential equations.

Keywords: Benjamina Bona Mohany equation; convection diffusion equation; collocation points; numerical problems; improvement factor; new modified Taylor wavelets.

DOI: 10.1504/IJANS.2024.141371

International Journal of Applied Nonlinear Science, 2024 Vol.4 No.3, pp.241 - 268

Accepted: 27 Mar 2024
Published online: 09 Sep 2024 *

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