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

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