Exponentially fitted variable two-step BDF algorithm for first order ODEs Original Research Article

We construct the exponential fitting extension of the classical variable step-size two-step BDF algorithm and examine its properties. We give the expression of the optimal value of the associated frequency and introduce a procedure for choosing the step widths in terms of the required accuracy. The order of the new algorithm is three (that is by one unit higher than for the classical one). On three severe stiff test cases we show that the new two-step algorithm behaves much better than its classical companion and that it is as good as the classical variable three-step algorithm.