On the Stability of Exponential Fitting BDF Algorithms: Higher-Order Methods

Abstract

The exponential fitting is a procedure to modify the classical algorithms in a way to make them particularly efficient for solving differential equations with oscillatory solutions or stiff problems. This chapter discusses a particular fast way to construct the coefficients to adapted BDF algorithms with constant steplength to these kind of problems. It examines the gain to be expected when vectorial first order ODE's are solved by BDF methods whose weights are generated by means of exponential fitting. The chapter shows some plots of zero-stability and absolute-stability of higher-order methods.