Ordinary Differential Equation Toolbox: ODEbox Version 1.1

This is a toolbos for the solution of ordinary differential equations including IVPs and BVPs.
Updated 17 Jun 2013

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Ordinary Differential Equations Toolbox: ODEbox

Matthew Harker and Paul O'Leary
University of Leoben

Version V1.1

This is a toolbox for the solution of ODEs. It includes methods for the solution of
initial-, boundary-, and innner-value problems. A special tool for the solution of IVPs is also provided, it makes it easy to solve IVPs both with constant and variable coefficients.

This toolbox requires the functions made available in the DOPbox:


You should download the ODEBox and the DOPbox and place both in the MATLAB path.

The library is organized as follows:

1) Documentation: This is the directory where you should start

2) ODEbox: is the directory containing the new functions required for the solution of the ODEs

The following directories contain a selection of examples for ODEs solved using this package.

3) IVPExamples: Thsi and the subdirectories contain three esamples on the use of the tool to solve IVPs

4) BVPExamples: This directory contains an example of solving a classical Engineering boundary value problem using the toolbox.

5) SturmLiouville: Contains three examples of Sturm-Liouville problems solved using the ODEbox.

The theory behind the functions in this library can be found in the paper:

Title: A Matrix Framework for the Solution of ODEs: Initial-, Boundary-, and
Inner-Value Problems
Authors: Matthew Harker and Paul O'Leary
Categories: math.NA
Comments: 20 pages
MSC-class: 15B02, 30E25, 65L60, 65L10, 65L15, 65L80

This paper can be found on-line at: http://arxiv.org/abs/1304.3312

The theory is also related to the paper.

author = {Paul O'Leary and Matthew Harker},
title = {A Framework for the Evaluation of Inclinometer Data in the
Measurement of Structures},
journal = {IEEE T. Instrumentation and Measurement},
volume = {61},
number = {5},
year = {2012},
pages = {1237-1251},
ee = {http://dx.doi.org/10.1109/TIM.2011.2180969}}

Some of the theory behind the local differential operators can be found in:

Author = {O'Leary, P. and Harker, M.},
Title = {Discrete Polynomial Moments and Savitzky-Golay Smoothing},
BookTitle = {Waset Special Journal},
Volume = {72},
DOI = {},
Pages = {439--443},
Year = {2010}}

The PDF is available at



All the PDF documentation in this library has been generated directly
from the m-files using the tool publish2latex available at:


Version 1.1

1) Upper and lower limits by odeSolveIVP tested to ensure that xMax is larger than xMin.
2) A number of typing errors have been correected.

April 2013 Paul O'Leary and Matthew Harker

Cite As

Matthew Harker, Paul O'Leary, (2024). Ordinary Differential Equation Toolbox: ODEbox Version 1.1 (https://www.mathworks.com/matlabcentral/fileexchange/41354-ordinary-differential-equation-toolbox-odebox-version-1-1), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2012a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes

1) Upper and lower limits by odeSolveIVP tested to ensure that xMax is larger than xMin.
2) A number of typing errors have been correected.