Variable-stepsize methods are constructed by extending a given fixed stepsize formula to a variable-stepsize formulation. The implementation of a multistep method requires finding an approximating polynomial for the solution of the ODE. We can view all implicit multistep formulas as piecewise polynomial collocation methods. This allows us to construct parametrized variable-stepsize formulas which include all possible k-step formulas of order k+1. Changing the formula in a code is then equivalent to changing the value of the parameters, and this could be fined-tuned to attain specific accuracy and stability properties. We also study the relation of the parameters to the error constants and the stability regions of the methods.

MINISIMPOSIUM SESSION: 19. Representation and implementation of variable step multistep methods