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version 1.1 (126 KB) by Meysam Mahooti
Adams-Bashforth-Moulton integration (8th order)


Updated 25 Dec 2018

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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.

Cite As

Meysam Mahooti (2019). Adams-Bashforth-Moulton (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (8)


kindly we will be thankful if you upload the reduction program please. Many students need to reduce higher (third or fourth) order ODEs to the system of first order ODEs using Matlab. We will be appreciated if you assist us.

symbolic toolbox required so useless

terry moore

Demi Moore



Revised on 2018-12-25.

Accuracy assessment is added to ABM8_test.m

MATLAB Release Compatibility
Created with R2018a
Compatible with any release
Platform Compatibility
Windows macOS Linux

Adams Bashforth Moulton 8th order