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Due to the widespread use of differential equations, numerical methods are being developed in order to solve numerous difficult initial value problems (IVPs) when an analytical solution would seem to be impractical. The goal of this study was to employ Taylor series expansion to construct a 2-point fully implicit block backward differentiation formula (2IBBDF), examine its stability characteristics and then apply the suggested approach to one of the models for tumor-immune interaction that are already in existence. Regarding the resolution of the tumor-immune interaction model, the research has compared the numerical outcomes of the suggested method with some of the current methodologies. The proposed technique outperforms the Ode15s and 2-point block backward differentiation formula (BBDF) in relation to accuracy in the scale error and in most of computational time. 

A-stability, implicit block method, ordinary differential equations, tumor-immune interaction model.