An Algorithm for Approximating Third-Order Ordinary Differential Equations with Applications to Thin Film Flow and Nonlinear Genesio Problems

Abstract

Third-order problems have been found to model real-life phenomena such as thick film fluid flow, boundary layer problems, and nonlinear Genesio problems, to name a few. This research focuses on the development of an algorithm using a basis function that combines an exponential function with a power series. This algorithm, called the Exponential Function Induced Algorithm (EFIA), was formulated using the collocation and interpolation techniques. The theoretical analysis of the algorithm was also carried out in this research. The outcome of the analysis showed that the algorithm is consistent, convergent, and zero-stable. The EFIA was applied to solving some real-life third-order problems like thin film flow and nonlinear Genesio problems. The numerical and graphical results obtained showed that the EFIA is accurate, has high precision, and is easy to implement. Algorithm, Exponentially-fitted function, Hybrid block method, Nonlinear Genesio equations, Thin film flow problem, Third-order