Algorithm of modified variable step block backward differentiation formulae for solving first order stiff ODEs

This paper presents a new method known as modified variable step block backward differentiation formulae (MVS-BBDF) for solving first order stiff Ordinary Differential Equations (ODEs). This solver utilizes the variable step size scheme for selecting the appropriate step size at each step of iteration. The development of an algorithm for numerical computation is elaborated in detail in this paper. Then, the numerical experiments are carried out to clarify the efficiency of our solver in comparison with the former method, variable step 2-point block backward differentiation formula (BBDF) and Matlab’s suite of ODE solvers, ode15s and ode23s. Consequently, the numerical results have proven that the introduced solver is also reliable in solving first order stiff ODEs.