Adams-Bashforth-Moulton

Adams-Bashforth-Moulton 8th Order Integration

This MATLAB package provides a compact, transparent implementation of 8th-order Adams-Bashforth-Moulton integration for orbital dynamics and other smooth initial-value problems. Unlike black-box solvers, the code exposes the predictor-corrector structure, derivative history handling, Runge-Kutta startup procedure, MATLAB ODE-style driver interface, fixed-step acceleration path, and variable-step ABM formulation, making it useful for researchers who want to study, modify, or benchmark multistep integration methods directly.

The included benchmark against MATLAB's ode113 provides an immediate way to evaluate accuracy and CPU time for a normalized Kepler problem with an analytical reference solution. Tolerances are supplied through odeset, and odeABM8 supports MATLAB-style vector tspan output, returning t and y at requested output times such as span = 0:60:3600. Because the implementation is modular, researchers can replace the force model, adjust tolerances, inspect intermediate histories, or extend the method toward more advanced variable-step and variable-order schemes while keeping the workflow simple and reproducible.

References

E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd ed., Springer, 1993.

L. F. Shampine and M. K. Gordon, Computer Solution of Ordinary Differential Equations: The Initial Value Problem, W. H. Freeman, 1975.

A. C. Hindmarsh et al., SUNDIALS: Suite of Nonlinear/Algebraic Equation Solvers, ACM Transactions on Mathematical Software, 31(3), 363-396, 2005.