Fakulti Ekonomi dan Muamalat, Universiti Sains Islam Malaysia, Nilai, Negeri Sembilan, Malaysia.
Centre of Foundation Studies for Agricultural Science, Putra University of Malaysia, Serdang, Selangor, Malaysia.
PLoS One. 2021 Feb 12;16(2):e0246904. doi: 10.1371/journal.pone.0246904. eCollection 2021.
Differential equations are commonly used to model various types of real life applications. The complexity of these models may often hinder the ability to acquire an analytical solution. To overcome this drawback, numerical methods were introduced to approximate the solutions. Initially when developing a numerical algorithm, researchers focused on the key aspect which is accuracy of the method. As numerical methods becomes more and more robust, accuracy alone is not sufficient hence begins the pursuit of efficiency which warrants the need for reducing computational cost. The current research proposes a numerical algorithm for solving initial value higher order ordinary differential equations (ODEs). The proposed algorithm is derived as a three point block multistep method, developed in an Adams type formulae (3PBCS) and will be used to solve various types of ODEs and systems of ODEs. Type of ODEs that are selected varies from linear to nonlinear, artificial and real life problems. Results will illustrate the accuracy and efficiency of the proposed three point block method. Order, stability and convergence of the method are also presented in the study.
微分方程常用于模拟各种类型的实际应用。这些模型的复杂性往往会阻碍获得解析解的能力。为了克服这一缺点，引入了数值方法来近似求解。在开发数值算法时，研究人员最初专注于方法的准确性这一关键方面。随着数值方法变得越来越强大，仅仅准确性是不够的，因此开始追求效率，这就需要降低计算成本。本研究提出了一种求解初值高阶常微分方程（ODE）的数值算法。所提出的算法是作为三点分组多步方法推导出来的，采用 Adams 型公式（3PBCS），并将用于求解各种类型的 ODE 和 ODE 系统。选择的 ODE 类型从线性到非线性、人为和现实生活问题不等。结果将说明所提出的三点分组方法的准确性和效率。该研究还介绍了该方法的阶数、稳定性和收敛性。
