Explicit advanced step-point (EAS) methods and the EAS2 multistep scheme for the solution of non-stiff initial value problems

In this work, we comprehensively examine, for the first time in a paper, the EAS2 methods, which are part of the explicit advanced step-point (EAS) family of methods. The EAS formulae comprise three distinct schemes: EAS1, EAS2 and EAS3. In this paper, we consider the EAS2 methods, which are meticulously studied and assessed and their superior regions of absolute stability are presented. Crucially, the computational efficiency of EAS2 is thoroughly examined and comparative numerical results are presented with the use of a variable step, variable order EAS2 code. The efficiency of EAS2 is measured against the established and powerful Adams formulae, as the latter were implemented in the Shampine and Gordon code. The extensive numerical results provide good evidence that EAS2 is competitive (i.e. faster and more accurate on a majority of test problems) with the well-established Adams methods for the numerical solution of non-stiff initial value problems.