The Approximate Numerical Solutions to First Order Non-Linear Differential Equations and Their Connections to the Orthogonal Double Cover in Graph Theory

Abstract

The main objective of this study is to make a linkage between Bernoulli's differential equations and graph theory using simple technique. Firstly, we transform an Orthogonal Double Cover (briefly, ODC) to metric graph. Then, we use the Generalized Fibonacci Polynomials (GFP) to transform the non-linear differential equation into a system of equations with undetermined constants. As a conclusion, some numerical examples were solved and the error was evaluated which prove the accuracy of the studied method.