Redefine trigonometric cubic B-spline collocation scheme for solving convection-diffusion equation Online publication date: Fri, 05-Apr-2024
by Ashish Kumar Rawat; Neeraj Dhiman; Anand Chauhan; Saumya Gupta
International Journal of Computing Science and Mathematics (IJCSM), Vol. 19, No. 3, 2024
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.
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