Composite backward differentiation formulas for solving stiff ordinary differential equation

In this study, a composite backward differentiation formula (BDF) is derived for solving stiff ordinary differential equations with initial condition given. In principle, the proposed method is built based on composite time integration methods combining the implicit Euler’s method and second order BDF, which are interleaved with interpolation polynomial procedure on intermediate solutions. The performance of the proposed method is validated by solving stiff initial value problems, where the accuracy is compared to the classical BDF in terms of absolute, maximum, and average errors. In conclusion, the composite BDF is a very promising method for solving stiff ordinary differential equations.