Malaysian Journal of Mathematical Sciences, June 2026, Vol. 20, No. 2
A Convergent and \(A-\)stable Three-sub-steps Composite Block Backward Differentiation Formula for Solving Stiff Differential Equations
Jaafar, B. A., Mohd Zawawi, I. S.
Corresponding Email: iskandarshah@uitm.edu.my
Received date: 23 June 2025
Accepted date: 12 December 2025
Abstract:
A novel composite block backward differentiation formula of order four, known as CBBDF(4), has been developed to effectively solve stiff differential equations. This self-starting method approximates solutions by evaluating two points simultaneously at each integration step, incorporating two intermediate points among the interpolating values. The CBBDF(4) scheme is structured through three sub-steps: in the first and second stages, Euler's method computes the intermediate values, setting up the third stage for applying the CBBDF(4) method. The derived method has been established to be convergent and \(A-\)stable, making it well-suited for solving stiff problems. To validate the method's accuracy and efficiency, several stiff initial value problems are solved using various step sizes. The numerical results are compared with the existing method in terms of maximum error, average error and computational time. Comparative analysis indicates that the new composite block method is not only practical but also successful in delivering reliable results.
Keywords: composite block scheme; linear multi-sub-step; stiff differential equations; three-sub-steps.
