Modified higher order block backward differentiation formula for third order ordinary differential equations

This study is aimed to modify higher order block backward differentiation formulae for dealing with the third order stiff ordinary differential equations (ODEs). Two new solutions are acquired at each step by using a few back values in preceding blocks. Apart from that, the differentiation coefficients will be stored, thus, repetitive calculations of the coefficients can be avoided as well as computational cost can also be optimized. A comparative analysis will be presented once the numerical experiments have been conducted to a few considered problems in order to confirm the efficiency of the proposed method with the existing stiff ODE solver. The analysis proves the accuracy and efficiency of the proposed method can be served as another alternative for third order stiff ODEs.