Mathematics and Statistics 10(5): 942-955, 2022 http://www.hrpub.org DOI: 10.13189/ms.2022.100506 Accuracy Improvement of Block Backward Differentiation Formulas for Solving Stiff Ordinary Differential Equations Using Modified Versions of Euler's Method Nurfaezah Mohd Husin 1 , Iskandar Shah Mohd Zawawi 1,* , Nooraini Zainuddin 2 , Zarina Bibi Ibrahim 3 1 Faculty of Computer & Mathematical Sciences, Kompleks Al-Khawarizmi, Universiti Teknologi MARA, Selangor, Malaysia 2 Mathematical and Statistical Sciences, Institute of Autonomous System, Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Perak, Malaysia 3 Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor, Malaysia Received June 6, 2022; Revised August 16, 2022; Accepted August 30, 2022 Cite This Paper in the Following Citation Styles (a): [1] Nurfaezah Mohd Husin, Iskandar Shah Mohd Zawawi, Nooraini Zainuddin, Zarina Bibi Ibrahim , "Accuracy Improvement of Block Backward Differentiation Formulas for Solving Stiff Ordinary Differential Equations Using Modified Versions of Euler’s Method," Mathematics and Statistics, Vol. 10, No. 5, pp. 942 - 955, 2022. DOI: 10.13189/ms.2022.100506. (b): Nurfaezah Mohd Husin, Iskandar Shah Mohd Zawawi, Nooraini Zainuddin, Zarina Bibi Ibrahim (2022). Accuracy Improvement of Block Backward Differentiation Formulas for Solving Stiff Ordinary Differential Equations Using Modified Versions of Euler’s Method. Mathematics and Statistics, 10(5), 942 - 955. DOI: 10.13189/ms.2022.100506. Copyright©2022 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract In this study, the fully implicit 2-point block backward differentiation formulas (BBDF) method has been successfully utilized for solving stiff ordinary differential equations (ODEs) by taking into account the uses of new starting methods namely, modified Euler’s method (MEM), improved modified Euler’s method (IMEM), and new Euler’s method (NEM). The reason of proposing the BBDF is that the method has been proven useful for stiff ODEs due to its A-stable properties. Furthermore, the method is able to approximate the solutions at two points simultaneously at each step. The proposed method is also implemented through Newton’s iteration procedure, which involves the calculation of the Jacobian matrix. Accuracy of the method is evaluated based on its performance in solving linear and non-linear initial value problems (IVPs) of first order stiff ODEs with transient and steady-state solutions. Some comparisons are made with the conventional BBDF approach for indicating the reliability of the proposed method. Numerical results indicate that not only classical Euler’s method provides accurate solutions for BBDF, but also the numerous modified versions of Euler’s methods improve the accuracy of BBDF, in terms of absolute error at certain step size and stage of iteration. Keywords Block Method, Ordinary Differential Equations, Stiff, Euler’s Method 1. Introduction The ordinary differential equations (ODEs) involve ordinary derivatives of one or more dependent variables with respect to a single independent variable [1]. The initial value problems (IVPs) of first-order ODEs can be represented in the following form: 0 ' ( , ), (0) , = = = d y t y dt y fy y (1) where the vector of variables, () () () () ( ) 1 1 , , , , n n t y t y t y t = ∈ y   describes n properties of interest in system, evolving for times 0 ≥ t starting from the initial value 0 (0) = y y . A special class of ODEs is known as stiff ODEs, which