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Please explain Matlab's naming convention for odepq

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There are ODE solvers built into Matlab, all named in the form of odepq.
I understand p is the order. For Euler's method it is order 1, Heun's and Midpoint are order 2, while Runge-kutta is order 4. What is the q here?

Accepted Answer

Walter Roberson
Walter Roberson on 22 Jan 2021
Edited: Walter Roberson on 22 Jan 2021
p is the order of the calculation used to predict the solution, and q is the order of the calculation used for the error estimate.
Exception:
"ode113 is a variable-step, variable-order (VSVO) Adams-Bashforth-Moulton PECE solver of orders 1 to 13. The highest order used appears to be 12, however, a formula of order 13 is used to form the error estimate and the function does local extrapolation to advance the integration at order 13."
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