A family of numerical multistep methods with three distinct schemes: explicit advanced step-point (EAS) methods and the EAS1 approach

Abstract

In this work, for the first time in an article, we present in a comprehensive way the explicit advanced step-point (EAS) methods. The EAS methods is a family of methods designed for the numerical solution of non-stiff and mildly stiff initial value problems (IVPs) and comprises three distinct schemes: EAS1, EAS2 and EAS3. A thorough theoretical analysis of the EAS family of predictor–corrector methods is presented in terms of their accuracy and stability characteristics and requirements, as well as the rationale for creating the three distinct schemes mentioned above. In this paper we also examine in detail one of the three schemes, the EAS1 methods. EAS1 are assessed for the very first time, are meticulously studied and their superior regions of absolute stability are presented. Furthermore the computational efficiency of EAS1 is examined and comparative numerical results are presented with the use of a variable step, variable order EAS1 code. The numerical results provide good evidence that EAS1 could be seen as superior to the well established Adams methods for the numerical solution of mildly stiff initial value problems.