The Adams-Bashforth-Moulton Integration Methods Generalized to an Adaptive Grid

Abstract

We present a generalization of the Adams-Bashforth-Moulton predictor-corrector numerical integration methods to an adaptive grid. The step size may be chosen dynamically in order to maintain a desired relative magnitude of error in each step. We demonstrate that the methods remain convergent to the expected degree, and apply various methods to the famous problem of determining the maximum possible mass of a neutron star supported by pure fermionic exclusion pressure. We reproduce the Tolman-Oppenheimer-Volkoff result of 0.71 solar masses using only 23 integration steps, and reproducing both mass and radius within 1% requires 27. We also present various optimizations and features of our implementation.