Wavelet-numerical hybrid scheme for delayed Lotka-Volterra equations: a Vieta–Fibonacci wavelet approach

Abstract In this paper, we introduce an innovative hybrid numerical scheme that combines the Vieta–Fibonacci wavelet with the Newton-Raphson method to solve the non-linear Lotka-Volterra predator–prey model with discrete delays. The proposed approach leverages the Vieta–Fibonacci operational matrix of integration to transform the model into a system of non-linear algebraic equations, which are efficiently solved using the Newton-Raphson method. Numerical results are compared with existing methods in the literature, demonstrating the superior accuracy of the proposed scheme. Absolute residual errors for both prey and predator species are computed across multiple test examples, consistently showing lower errors than those of established techniques. The method provides notable benefits, including ease of implementation and optimized memory usage owing to the sparse nature of the operational matrix. Additionally, increasing the number of collocation points further improves the precision of approximations for both species.