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The numerical integrator has a large number of member functions defined for various purposes. There are functions to set up the initial conditions; others to set up the integrator and perform the integration; access operators to report the output or any problems that have been encountered; and reset functions to repeat the integration.
Table 1 gives a brief description of the general nature of each group of functions. The actual functions are defined in the sections to follow. For each, the usage is defined, along with any required or optional inputs, and a description of the purpose of the routine and any special considerations in using it.
Table 1 Numerical Integrator Function Classifications.
Class 
Description 
Section 
Constructor 
The constructor is called when the numerical integrator object is created. It initially prepares the integrator for use. 
2.3 
Integration Functions 
These functions are called to perform the actual integration. Also included is a function that returns true when integration is complete. 
2.4 
Step Size Control Functions 
These functions set the minimum, maximum, and initial step sizes. They also specify whether fixed or variable step lengths are to be used. They also specify which variable step method to use. 
2.5 
Step Size Information Functions 
These functions return the values of minimum, maximum, initial, and current step size. There are also accessors which tell if the steps are fixed or variable, which variable step method is in use, and whether integration is forward or backward in time. 
2.6 
Error Tolerance Control Functions 
These functions set the absolute and relative error tolerances, and specify which norm to use. 
2.7 
Error Tolerance Information Functions 
These functions return the absolute and relative error tolerances, which norm is in use, the current error estimate, and a scale factor by which the tolerances need to be multiplied to satisfy the error requirements. 
2.8 
Initial Condition Functions 
These functions set and return the initial conditions. 
2.9 
Output Control Functions 
These functions tell the integrator when to output the state variables, and whether to let the ODE handle output. 
2.10 
Output Functions 
These functions return the output from the integration as well as the current state of the integrator. 
2.11 
Event Handling Functions 
These functions tell the integrator whether to use event handling and how to output the results. 
2.12 
Event Output Functions 
These functions return the times, type, and values of the states at each event incident. 
2.13 
Integrator Limit Functions 
These functions set limits on how far the integration may proceed to keep it from taking too long because of an error or illconditioned problem. 
2.14 
Integrator Diagnostic Functions 
These functions provide information on the state of the integrator, such as how many steps and function evaluations have been performed. 
2.15 
Integrator Reset Functions 
These functions reset the integrator for reuse and allow you to install new ODE’s or Butcher Tables. 
2.16 
Functions to Check the 
These functions allow you to check if any errors have occurred or if the integrator has received bad input. 
2.17 
Functions to Reset Specific Error States 
These functions allow you to reset certain errors in order to continue integration. 
2.18 
Exceptions 
An exception class for throwing errors. 
2.19 
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