A proposed sixth order inverse polynomial method for the solution of non-linear physical models

Abstract

There are several nonlinear physical models emanated from science and technology that have always remained a challenge for numerical analysts and applied mathematicians. Various one-step numerical methods were developed to deal with these models, however, it requires the developed method to have consistency, stability, zero stability and convergence characteristics to handle the non-linearity in the model. This paper proposes a new sixth order inverse polynomial method (SOIPM) with a relative measure of stability for the solution of non-linear physical models with different flavors. Firstly, the properties of SOIPM are analyzed and investigated. Moreover, three illustrative non-linear physical models have been solved to measure the accuracy, computational performance, suitability and effectiveness of SOIPM. Furthermore, the results generated via SOIPM are compared with the existing method of the celebrated Runge-Kutta of order four (RK4) in the context of the exact value (EV). Finally, the absolute errors (ABEs) and final absolute errors (FABEs) incurred by SOIPM are computed and compared with that of RK4.