A Gautschi-type method for oscillatory second-order differential equations
The authors study a numerical method for second-order differential equations in which high-frequency oscillations are generated by a linear part. The scheme is based on the requirement that it solves linear problems with constant inhomogeneity exactly (Gautschi-type method). It is proved that the method admits second-order error bounds which are independent of the product of the stepsize with the frequencies. Results of numerical experiments with the sine-Gordon equation are included.
oscillatory second-order differential equations
scientific article; zbMATH DE number 1355440