The numerical solution of a time-delay model of population growth with immigration using Legendre wavelets

The paper addresses a computational method to simulate more accurate models for population growth with immigration, focusing on integral equations (IEs) featuring a delay parameter in the time variable. The proposed method utilizes Legendre wavelets within the Galerkin scheme as a orthonormal basis. Legendre wavelets are known for their localized functions, offering suitable precision and stability in simulating time-delay biological models. This approach employs the composite Gauss-Legendre (CGL) quadrature rule to compute integrals appeared in the scheme. An error bound analysis demonstrates a convergence rate of order 2-Mk. Additionally, various numerical examples are presented to show the efficiency, accuracy and validate the theoretical error estimate of the novel technique.

Automated summary

This paper presents a computational method for simulating more accurate models for population growth with immigration, using integral equations with a delay parameter. The method utilizes Legendre wavelets within the Galerkin scheme as an orthonormal basis and employs the composite Gauss-Legendre quadrature rule for computing integrals. An error bound analysis demonstrates the convergence rate of the method, and various numerical examples are provided to validate the efficiency and accuracy of the technique as well as the theoretical error estimate.