Numerical solution of several second-order ordinary differential equations containing logistic maps as nonlinear coefficients

TL;DR

This paper develops a numerical approach using the Numerov algorithm to solve second-order ODEs with logistic maps as nonlinear coefficients, analyzing the impact of initial conditions on solutions.

Contribution

It introduces a novel application of the Numerov method to ODEs with logistic map nonlinearities and explores initial condition effects.

Findings

Numerov algorithm effectively solves these nonlinear ODEs.

Initial conditions significantly influence solution behavior.

Logistic map nonlinearities introduce complex solution dynamics.

Abstract

This work is devoted to find the numerical solutions of several one dimensional second-order ordinary differential equations. In a heuristic way, in such equations the quadratic logistic maps regarded as a local function are inserted within the nonlinear coefficient of the function as well as within the independent term. We apply the Numerov algorithm to solve these equations and we discuss the role of the initial conditions of the logistic maps in such solutions.