Implicit r-point block backward differentiation formula for solving first-order stiff ODEs

In this paper, we consider an implicit r-point block backward differentiation formula (BBDF) methods for solving ordinary differential equations (ODEs). A block of r new values at each step are derived. A performance comparison of the r-point block methods is compared with the existing backward differentiation formula (BDF) method. Numerical results indicate that the r-point BBDF method is more efficient in improving CPU time and reduce the number of integration step.