Solutions of BVPs arising in hydrodynamic and magnetohydro-dynamic stability theory using polynomial and non-polynomial splines

This paper describes the exceptionally precise results of 6th-order and 8th-order nonlinear boundary-value problems(BVPs). Cubic-Nonpolynomial spline(CNPS) and Cubic-polynomial spline(CNPS) are utilized to solve such types of BVPs. We develop the class of numerical techniques for a particular selection of the factors that are associated with nonpolynomial and polynomial splines. Using the developed class of numerical techniques, the problem is reduced to a new system that consists of 2nd-order BVPs only. The end conditions associated with the BVPs are determined. For each problem, the results obtained by CNPS and CPS is compared with the exact solution. The absolute error(AE) for every iteration is calculated. To show that the suitable responses established by using CNPS and CPS have a higher level of preciseness, the absolute errors of the CNPS and CPS have been compared with different techniques such as DTM, ADM, Parametric septic splines, Variational-iteration method(VIM), Daftardar Jafari strategy, MDM, Cubic B-Spline, Homotopy method(HM), Quintic and Sextic B-spline and observed to be more accurate. Graphs that describe the graphical comparison of CNPS and CPS at n = 10 are also included in this paper. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.

Automated summary

This paper describes the precise results obtained by solving 6th and 8th-order nonlinear boundary-value problems using Cubic-Nonpolynomial spline (CNPS) and Cubic-polynomial spline (CPS). A class of numerical techniques is developed to simplify the problem to a new system consisting of 2nd-order BVPs, with comparisons made to exact solutions for accuracy validation. The results show that CNPS and CPS provide more accurate responses compared to other techniques.