Shampine-Gordon Integrator

Shampine-Gordon is a variable-step, variable-order multi-step integrator.
104 Downloads
Updated 18 Mar 2020

View License

Linear multi-step methods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial point and then takes a short step forward in time to find the next solution point. The process continues with subsequent steps to map out the solution. Single-step methods (such as Euler's method) refer to only one previous point and its derivative to determine the current value. Methods such as Runge–Kutta take some intermediate steps (for example, a half-step) to obtain a higher order method, but then discard all previous information before taking a second step. Multi-step methods attempt to gain efficiency by keeping and using the information from previous steps rather than discarding it. Consequently, multi-step methods refer to several previous points and derivative values. In the case of linear multi-step methods, a linear combination of the previous points and derivative values is used.
Here, integration of the normalized two-body problem from t0 = 0 to t = 86400(s) for an eccentricity of e = 0.1 is implemented by Shampine-Gordon (variable-step, variable-order multi-step integrator) and compared with MATLAB’s ode113 (variable order Adams-Bashforth-Moulton PECE solver).

Cite As

Meysam Mahooti (2024). Shampine-Gordon Integrator (https://www.mathworks.com/matlabcentral/fileexchange/74570-shampine-gordon-integrator), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2019b
Compatible with any release
Platform Compatibility
Windows macOS Linux
Tags Add Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes
1.0.0