Exploring the dynamics of a generalized Burgers–Fisher model with advection and diffusion utilizing finite volume and finite difference strategies
Year: 2025
Type: article
Abstract: This investigation presents a numerical arrangement for the generalized nonlinear Burgers–Fisher equation, utilizing both finite difference and finite volume strategies, which provide second-order spatial and transient precision. An implicit strategy is proposed to illuminate reaction–diffusion equations, where algebraic distinction conditions are illuminated at each time step utilizing iterative strategies to handle nonlinear frameworks. The soundness and joining of the strategies are assessed, and numerical results illustrate that the proposed finite volume approach is effective and dependable for solving nonlinear reaction–diffusion models. The numerical results demonstrate excellent agreement with analytical solutions obtained using the tanh–coth method. The displayed strategies exhibit higher accuracy, as assessed by L∞ error standards, and appear to enhance productivity by diminishing the network division at short temporal intervals. These approaches are appropriate for understanding nonlinear challenges in design and materials science.
Source: AIP Advances
DOI: 10.1063/5.0290978
Authors: Muhammad Saqib, Muzammal Saleem, Muhammad Abdullah, Shahid Hasnain, Muhammad Farman, Mohamed Hafez
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,350
OpenAlex ID: W4416316664