TY  - JOUR
AU  - Alhassan, Buhari
AU  - Hamisu, Musa
AU  - Saadu, Abubakar Sadiq
AU  - Kantsi, Kabiru Abubakar
PY  - 2026
DA  - 2026/09/09
TI  - Numerical Simulation of Stiff Systems of Ordinary Differential Equations Using a Block Extended Backward Differentiation Scheme with a Stability Control Parameter
JO  - Journal of Numerical Simulations in Physics and Mathematics
T2  - Journal of Numerical Simulations in Physics and Mathematics
JF  - Journal of Numerical Simulations in Physics and Mathematics
VL  - 2
IS  - 2
SP  - 69
EP  - 89
DO  - 10.62762/JNSPM.2026.422478
UR  - https://www.icck.org/article/abs/JNSPM.2026.422478
KW  - block extended backward differentiation formula
KW  - stiff ordinary differential equations
KW  - stability control parameter $\rho$
KW  - Newton’s iteration method
KW  - numerical solution
KW  - block methods
AB  - Stiff systems of ordinary differential equations (ODEs) arise frequently in several areas of applied mathematics, science, and engineering, and their numerical integration requires methods with strong stability characteristics. In this paper, a block extended backward differentiation formula (BEBDF) with a stability control parameter is developed for the numerical solution of stiff systems of ODEs. The proposed method is constructed within the framework of block multistep methods, allowing the simultaneous computation of solution values at several grid points. A free parameter $\rho$ is incorporated into the formulation of the method to regulate and improve its stability behavior. The presence of this parameter provides additional flexibility in controlling the stability properties of the scheme, which is particularly beneficial when dealing with stiff problems. The nonlinear system arising from the implementation of the proposed method is solved using Newton’s iteration technique to ensure efficient and reliable convergence. The computational algorithm for the method is implemented in the Dev-C++ compiler environment, where the block structure of the scheme facilitates efficient numerical computation. Furthermore, the fundamental properties of the method, including consistency, zero-stability, and convergence, are analyzed to establish its theoretical reliability. Numerical experiments performed on selected stiff test problems demonstrate that the proposed method produces accurate and stable results. The findings indicate that the inclusion of the free parameter $\rho$ significantly enhances the stability control and overall performance of the method in the numerical solution of stiff systems of ODEs.
SN  - 3068-9082
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Alhassan2026Numerical,
  author = {Buhari Alhassan and Musa Hamisu and Abubakar Sadiq Saadu and Kabiru Abubakar Kantsi},
  title = {Numerical Simulation of Stiff Systems of Ordinary Differential Equations Using a Block Extended Backward Differentiation Scheme with a Stability Control Parameter},
  journal = {Journal of Numerical Simulations in Physics and Mathematics},
  year = {2026},
  volume = {2},
  number = {2},
  pages = {69-89},
  doi = {10.62762/JNSPM.2026.422478},
  url = {https://www.icck.org/article/abs/JNSPM.2026.422478},
  abstract = {Stiff systems of ordinary differential equations (ODEs) arise frequently in several areas of applied mathematics, science, and engineering, and their numerical integration requires methods with strong stability characteristics. In this paper, a block extended backward differentiation formula (BEBDF) with a stability control parameter is developed for the numerical solution of stiff systems of ODEs. The proposed method is constructed within the framework of block multistep methods, allowing the simultaneous computation of solution values at several grid points. A free parameter \$\rho\$ is incorporated into the formulation of the method to regulate and improve its stability behavior. The presence of this parameter provides additional flexibility in controlling the stability properties of the scheme, which is particularly beneficial when dealing with stiff problems. The nonlinear system arising from the implementation of the proposed method is solved using Newton’s iteration technique to ensure efficient and reliable convergence. The computational algorithm for the method is implemented in the Dev-C++ compiler environment, where the block structure of the scheme facilitates efficient numerical computation. Furthermore, the fundamental properties of the method, including consistency, zero-stability, and convergence, are analyzed to establish its theoretical reliability. Numerical experiments performed on selected stiff test problems demonstrate that the proposed method produces accurate and stable results. The findings indicate that the inclusion of the free parameter \$\rho\$ significantly enhances the stability control and overall performance of the method in the numerical solution of stiff systems of ODEs.},
  keywords = {block extended backward differentiation formula, stiff ordinary differential equations, stability control parameter \$\rho\$, Newton’s iteration method, numerical solution, block methods},
  issn = {3068-9082},
  publisher = {Institute of Central Computation and Knowledge}
}