Akindeinde Saheed Ojo
Department of Mathematics, Obafemi Awolowo University, 220005, Ile-Ife, Nigeria.
Heliyon. 2020 Oct 13;6(10):e05188. doi: 10.1016/j.heliyon.2020.e05188. eCollection 2020 Oct.
The article introduces a new multistage technique for solving a polynomial system of nonlinear initial and boundary value problems of differential equations. The radius of convergence of the series solution to the problem is derived a-priorly in terms of the parameters of the polynomial system. Then guided by the convergence-control parameter , the domain of the problem is split into subintervals. By stepping out in a multistage manner, corresponding subproblems are defined which are then subsequently solved with conventional Parker-Sochacki method to get a piecewise continuous solution with very high accuracy. The method is applied to SIR epidemic model, stiff differential equation modelling combustion, Lorenz chaotic problem, and the Troesch's boundary value problem. The results obtained showed a remarkable accuracy when compared with Runge-Kutta Method of order 4. The article showcased the proposed method as a simple, yet accurate approximate analytical technique for nonlinear differential equations.
本文介绍了一种新的多阶段技术，用于求解微分方程非线性初值和边值问题的多项式系统。该问题级数解的收敛半径根据多项式系统的参数先验推导得出。然后，在收敛控制参数的引导下，将问题的定义域划分为子区间。通过多阶段推进，定义相应的子问题，随后用传统的帕克 - 索查基方法求解，以获得具有非常高精确度的分段连续解。该方法应用于SIR传染病模型、模拟燃烧的刚性微分方程、洛伦兹混沌问题以及特罗斯奇边值问题。与四阶龙格 - 库塔方法相比，所得结果显示出显著的精确度。本文展示了所提出的方法是一种用于非线性微分方程的简单而精确的近似解析技术。
