Nawaz Yasir, Arif Muhammad Shoaib, Abodayeh Kamaleldin, Ashraf Muhammad Usman, Naz Mehvish
Department of Mathematics, Air University, PAF Complex E-9, Islamabad, 44000, Pakistan.
Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia.
Heliyon. 2023 Oct 12;9(10):e20868. doi: 10.1016/j.heliyon.2023.e20868. eCollection 2023 Oct.
This article suggests a fourth-order numerical approach for solving ordinary differential equations (ODEs) that are both linear and nonlinear. The suggested scheme is an explicit predictor-corrector scheme. For linear ODE, the proposed numerical scheme's stability area is discovered. The proposed strategy yields the same stability region as the traditional fourth-order Runge-Kutta method. In addition, partial differential equations (PDEs) are used to develop the mathematical model for the flow of non-Newtonian micro-polar fluid over the sheet and heat and mass transit using electric field effects. These PDEs are further transformed into dimensionless boundary value problems. Boundary value problems are resolved using the proposed shooting-based scheme. The findings show that increasing values of ion kinetic work and Joule heating parameters cause the temperature profile to climb. The results produced by the suggested strategy are compared to those discovered through earlier studies. The results of this study could serve as a starting point for future fluid-flow investigations in a secure industrial environment.
本文提出了一种用于求解线性和非线性常微分方程（ODE）的四阶数值方法。所建议的方案是一种显式预测-校正方案。对于线性ODE，发现了所提出数值方案的稳定区域。所提出的策略产生的稳定区域与传统的四阶龙格-库塔方法相同。此外，使用偏微分方程（PDE）建立了非牛顿微极流体在平板上流动以及考虑电场效应的热质传递的数学模型。这些PDE进一步转化为无量纲边值问题。使用所提出的基于打靶的方案解决边值问题。结果表明，离子动力学功和焦耳热参数值的增加会导致温度分布上升。将所提出策略产生的结果与早期研究中发现的结果进行比较。本研究的结果可为未来在安全工业环境中的流体流动研究提供一个起点。
