TY  - JOUR
IS  - 5
N2  - 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 Eulerâ??s method (MEM), improved modified Eulerâ??s method (IMEM), and new Eulerâ??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 Newtonâ??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 Eulerâ??s method provides accurate solutions for BBDF, but also the numerous modified versions of Eulerâ??s methods improve the accuracy of BBDF, in terms of absolute error at certain step size and stage of iteration. © 2022 by authors. All rights reserved.
ID  - scholars16419
UR  - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85137325686&doi=10.13189%2fms.2022.100506&partnerID=40&md5=939bda5f01480048ca87ee9df7a82a06
A1  - Husin, N.M.
A1  - Zawawi, I.S.M.
A1  - Zainuddin, N.
A1  - Ibrahim, Z.B.
JF  - Mathematics and Statistics
VL  - 10
Y1  - 2022///
N1  - cited By 0
TI  - Accuracy Improvement of Block Backward Differentiation Formulas for Solving Stiff Ordinary Differential Equations Using Modified Versions of Euler's Method
SP  - 942
AV  - none
EP  - 955
SN  - 23322071
PB  - Horizon Research Publishing
ER  -