Shampine-Gordon Integrator

Shampine-Gordon is a variable-step, variable-order multi-step integrator.

This MATLAB implementation of the Shampine-Gordon method provides researchers with a transparent and accessible variable-order, variable-step ODE solver that follows the familiar ode113 calling style. Because the algorithm is implemented directly in MATLAB, users can inspect, modify, and extend the numerical procedure without relying on compiled or hidden solver internals, making it especially useful for teaching, verification, reproducibility studies, and method comparison.

The code is particularly suitable for astrodynamics and orbital mechanics applications, where accurate long-term integration and controlled error behavior are essential. The included Keplerian test problem, analytical reference solution, and comparison with MATLAB's ode113 provide researchers with a ready starting point for validating their own dynamical models and assessing solver performance under practical conditions.

Reference

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