Exploring the dynamics of a generalized Burgers–Fisher model with advection and diffusion utilizing finite volume and finite difference strategies

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.