Linear Multistep Methods with Reduced Truncation Error for Periodic Initial-value Problems

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Abstract
A common feature of most methods for numerically solving ordinary differential equations is that they consider the problem as a standard one without exploiting specific properties the solution may have. Here we consider initial-value problems the solution of which is a priori known to possess an oscillatory behaviour. The methods are of linear multistep type and special attention is paid to decreasing the value of those terms in the local truncation error which correspond to the oscillatory solution components. Numerical results obtained by these methods are reported and compared with those obtained by the corresponding conventional linear multistep methods and by the methods developed by Gautschi.

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