Symmetric linear multistep methods for second-order differential equations with periodic solutions

Abstract

Special symmetric linear multistep methods for second-order differential equations without first derivatives are proposed. The methods can be tuned to a possibly a priori knowledge of the user on the location of the frequencies, that are dominant in the exact solution. On the basis of such extra information the truncation error can considerably be reduced in magnitude. Numerical results are compared with results produced by the symmetric methods of Lambert and Watson and the method of Gautschi.