On Comparison of Algorithms Techniques for Numerical Solutions of Higher Order Differential Equations

Abstract:

Higher order differential equations appear in many different fields such as engineering, biology, chemistry, and the physical sciences. Obtaining numerical analysis solutions for different models in different applied mathematics plays an important role in explaining various applied phenomena such as beam analysis in civil engineering, pendulum mathematics in physics, thermo-liquid dynamics, stochastic modelling, plasma and nuclear physics, and nonlinear optics. In this paper, we build and implement four computational algorithms (exponential fitted collocation algorithm, differential transformation algorithm, homotopy perturbation algorithm and new iterative algorithm) for the numerical solutions of higher order differential equations from applied mathematics. The resulting numerical solutions were presented as 2D functional graphs using MAPLE 18 software to demonstrate the real world significance of the presented equations. The proposed algorithms required less computation time and the obtained results demonstrated that the algorithms are suitable for use for other higher order differential equations in applied mathematics and are efficient in terms of applications use.