Special methods for problems whose oscillatory solution is damped (Q1119344)

The authors investigate linear multistep methods tailored for ordinary differential equations whose solution behaves like a linear combination of exponential functions. The methods are constructed using trigonometric fitting approach investigated before by Gautschi and minimax approach developed by van der Houwen and Sommeijer. The resulting systems of equations for the coefficients of the methods are solved by using MACSYMA or REDUCE symbolic manipulation packages. One numerical example is presented which compares first and second order methods obtained by different approaches.