The Solutions of Nonlinear Heat Conduction Equation via Fibonacci&Lucas Approximation Method

TL;DR

This paper introduces a Fibonacci and Lucas approximation method to find new exact travelling wave solutions for nonlinear heat conduction equations, expanding the solution space for physical systems.

Contribution

The study extends auxiliary equations to include Fibonacci and Lucas types, providing a novel approximation method for exact solutions of nonlinear PDEs.

Findings

New exact travelling wave solutions derived

Method produces a variety of solutions for physical systems

Enhanced solution techniques using Fibonacci & Lucas equations

Abstract

To obtain new types of exact travelling wave solutions to nonlinear partial differential equations, a number of approximate methods are known in the literature. In this study, we extend the class of auxiliary equations of Fibonnacci&Lucas type equations. The proposed Fibonnacci&Lucas approximation method produces many new solutions. Consequently, we introduce new exact travelling wave solutions of some physical systems in terms of these new solutions of the Fibonacci&Lucas type equation. In addition to using different ansatz, we use determine different balancing principle to obtain optimal solutions.