3 Point Block Backward Differentiation Formula with Multiple Off-Step Points for the Solution of Stiff Problems

Vanenchii Ayoo; Katmol Damap; Hassan Ibrahim

doi:10.62050/ljsir2025.v3n2.549

Authors

Vanenchii Peter Ayoo Department of Mathematics, Federal University of Lafia, PMB 146, Lafia, Nigeria Author
Katmol Yunana Damap Department of Mathematics, Federal University of Lafia, PMB 146, Lafia, Nigeria Author
Hassan Ibrahim Department of Mathematics, Federal University of Lafia, PMB 146, Lafia, Nigeria Author

DOI:

https://doi.org/10.62050/ljsir2025.v3n2.549

Keywords:

Backward Differentiation Formula, Block Multiple Off-Step Point , Linear Multistep Methods , Stiff Ordinary Differential Equations

Abstract

In this study, a three-point block backward differentiation formula (3PBBDF) method is derived for solving first-order stiff initial value problems (IVPs) of ordinary differential equations (ODEs). The newly proposed method is analyzed for its key properties and is found to be A-stable, zero-stable, and effective in handling stiff IVPs. To evaluate the performance of the 3PBBDF method, several stiff IVPs are solved, and the results are compared against existing numerical schemes. The comparison, based on tabulated results and plotted graphs, demonstrates that the proposed method offers superior accuracy in terms of error scaling over three competing methods and also outperforms two methods in terms of execution time. Consequently, the proposed 3PBBDF scheme proves to be an efficient tool for integrating stiff IVPs in ODEs

Downloads

Download data is not yet available.

References

Yusuf, H., Musa, H., & Alhassan, B. (2024). A New Fixed Coefficient Diagonally Implicit Block Backward Differentiation Formula for Solving Stiff Initial Value Problems A periodical of the Faculty of Natural and Applied Sciences , UMYU , Katsina A New Fixed Coefficient Diagonally Implicit Block Back. February. https://doi.org/10.56919/usci.2431.001

Alhassan, B., & Musa, H. (2023). Diagonally Implicit Extended 2-Point Super Class of Block Backward Differentiation Formula with Two Off-step Points for Solving First Order Stiff Initial Value Problems.

Soomro, H., Zainuddin, N., Daud, H., Sunday, J., & Jamaludin, N. (2022). Variable Step Block Hybrid Method for Stiff Chemical Kinetics Problems. https://doi.org/10.3390/app12094484

Ramos, H., & Rufai, M. A. (2024). A two-step hybrid block method with fourth derivatives for solving third- order boundary value problems. Journal of Computational and Applied Mathematics, February 2021, 113419.

Husin, N. M., Shah, I., Zawawi, M., Zainuddin, N., & Ibrahim, Z. B. (2022). Accuracy Improvement of Block Backward Differentiation Formulas for Solving Stiff Ordinary Differential Equations Using Modified Versions of Euler’s Method. 10(5), 942–955. https://doi.org/10.13189/ms.2022.100506

Abdullahi, M., Suleiman, S., & Masanawa, A. (2022). An A- Stable Block Integrator Scheme for the Solution of First Order System of IVP of Ordinary Differential Equations.16(4).https://doi.org/10.9734/APAS/2022/v16i430407

Sagir, A. M., & Abdullahi, M. (2022). A Robust Diagonally Implicit Block Method for Solving First Order Stiff IVP of ODEs. 11(1), 252–273.

Soomro, H., Zainuddin, N., Daud, H., & Sunday, J. (2023). 3 ‑ Point block backward differentiation formula with an off ‑ step point for the solutions of stiff chemical reaction problems. Journal of Mathematical Chemistry, 61(1), 75–97. https://doi.org/10.1007/s10910-022-01402-2

Khalsaraei, M. M., Shokri, A., & Molayi, M. (2020). Mohammad Mehdizadeh Khalsaraei , Ali. October 2020. https://doi.org/10.1007/s10910-020-01160-z

Ismail, G. A. F., & Ibrahim, I. H. (1999). New efficient second derivative multistep methods for stiff systems. 23