High order boundary value linear multistep method for the numerical solution of IVPs in ODEs

In this paper, we introduce High order boundary value linear multistep method (HOBVLMM) for the numerical solution of stiff systems of initial value problems (IVPs). The order, error constant, zero stability and the region of absolute stability for the HOBVLMM are discussed. The proposed scheme posses 0k,k-1 -stability and (Ak,k-1 )-stability, achieving a high order of p = 2k - 1, where k represents the step number of the LMM. The methods prove to be effective for stiff systems of IVPs in ordinary differential equations (ODEs), as evidenced by our numerical experiments, which shows superior performance compared to some existing methods.