Conclusions.
•HOSVS methods provide a useful method of combining the efficiency gains of both higher order and variable stepsize methods.
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•The CEOT method is the most efficient where 6th-8th order integrators, which accurately calculate the re-parameterisation function, are required.
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•The OEC method is useful for very high order integrators or where existing coefficients are to be used, which accurately calculate the re-parameterisation function.
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•The MO method is best suited, and the most efficient, where accurate determination of the re-parameterisation function is not important, such as time transformations based on the eccentricity of the orbit of Mercury.