Title: Redefine trigonometric cubic B-spline collocation scheme for solving convection-diffusion equation

Authors: Ashish Kumar Rawat; Neeraj Dhiman; Anand Chauhan; Saumya Gupta

Addresses: Department of Mathematics, Graphic Era Deemed to be University, Dehradun, 248002, India ' Department of Mathematics, Graphic Era Hill University, Dehradun, 248002, India ' Department of Mathematics, Graphic Era Deemed to be University, Dehradun, 248002, India ' Department of Management Studies, Graphic Era Deemed to be University, Dehradun 248002, India

Abstract: Redefining the formulation of the trigonometrical cubic B-spline, collocation-based scheme is used to approximate the numerical solution of the convection-diffusion partial differential equation (PDE). This proposed work is based on the usual discretisation of the linear and non-linear terms of the PDE. The Robin-Graves technique is used to linearise the non-linear terms of the PDE, whether initial values are recalled by the initial or boundary condition. The finite difference scheme applies to this work for discretised time variable terms of the convection-diffusion equation. To establish the scheme, an example is compared with existing results, and the comparison is finer than the existing result. In this paper, we propose a modern technique that has impressive results compared to the previous technique. In the future, malaria type convection equation will be simulated by a redefine trigonometric function with a collocation scheme to understand the increment phenomena of the malaria parasite.

Keywords: redefine trigonometric cubic B-spline; collocation method; convection diffusion equation; finite difference scheme; trigonometric basis function; Taylor series expansion; Robin-Graves technique.

DOI: 10.1504/IJCSM.2024.137829

International Journal of Computing Science and Mathematics, 2024 Vol.19 No.3, pp.244 - 255

Received: 25 Aug 2022
Accepted: 27 Jun 2023
Published online: 05 Apr 2024 *

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