Date of Publication :15th January 2025

Abstract: The backward differentiation formulae are considered as the most popular and the best class of linear multistep method s for handling stiff problems, however, they have their drawbacks as they are A – stable for k = 1, 2,A(α), stable for k = 3,... , 6 and non self – starting for k ≥ 2. This paper focused on the development and implementation of a new higher order numerical method by a modification of the backward differentiation formulae for the solutions of stiff initial value problems. The methodology used for the derivation of the new method was the multistep collocation approach, while the test equation approach was used to plot their regions of absolute stability. From the convergence analysis, the methods were consistent and zero – stable, hence convergent and of uniform order p = k. Also, results show that the eight step BMBDF were A- stable. The new method resolves the stability problem and overcomes the non self -starting property inherent in the standard backward differentiation formulae (BDF). The eight step BMBDF was applied to odes arising from real life and results show that they were efficient and accurate and compete well with other existing methods. Also, the solution curves of the eight step BMBDF compete well with the exact solutions and the well-known ode23 solver. Since the new method was A – stable, it was recommended for the solutions of stiff initial value problems resulting from real life.

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