MATLAB: Please explain Matlab’s naming convention for odepq

odeode45

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?

Best Answer

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."

Related Solutions

MATLAB: Ode45 : order, number of prediction and step time (theory)

ODE45 is a Runge-Kutta single step solver using the pair of order 4 and 5 solvers as communicated by Dormand and Prince. The parameters for the order 4 and 5 are chosen such, that the a minimum number of function evaluations is required.

The local discretization error is measured by the difference between the order 4 and 5 solutions. The time steps are chosen such, that this difference is smaller than the given relative and absolute tolerances.

You can find all details by reading the code of ODE45, especially the references will be helpful.

MATLAB: Is there a fixed-step Ordinary Differential Equation (ODE) solver in MATLAB 8.0 (R2012b)

The ability to use a fixed-step solver is not built into MATLAB 8.0 (R2012b).

The ordinary differential equation solver functions provided with MATLAB employ a variety of variable-step methods. ODE23 is based on the Runge Kutta (2,3)integration method, and ODE45 is based on the Runge Kutta (4,5) integration method. ODE113 is a variable-order Adams-Bashforth-Moulton PECE solver. For a complete listing of the various solvers and their methods, see the documentation.

The MATLAB ODE solvers utilize these methods by taking a step, estimating the error at this step, checking to see if the value is greater than or less than the tolerance, and altering the step size accordingly. These integration methods do not lend themselves to a fixed step size. Using an algorithm that uses a fixed step size is dangerous since you can miss points where your signal frequency is greater than the solver frequency. Using a variable step ensures that a large step size is used for low frequencies and a small step size is used for high frequencies. The ODE solvers within MATLAB are optimized for a variable step, run faster with a variable step size, and clearly the results are more accurate.

There are now fixed time step solvers available:

ODE1 - A first-order Euler method

ODE2 - A second-order Euler method

ODE3 - A third-order Runge-Kutta method

ODE4 - A fourth-order Runge-Kutta method

ODE5 - A fifth-order Runge-Kutta method

ODETest

These are included in the attached zip file. After saving the files into a folder located on the MATLAB path, these solvers can be used with the following syntax:

y = ode4(odefun,tspan,y0);

The integration proceeds by steps, taken to the values specified in tspan. The time values must be in order, either increasing or decreasing. Note that the step size (the distance between consecutive elements of tspan) does not have to be uniform. If the step size is uniform, you might want to use LINSPACE.

For example,

tspan = linspace(t0,tf,nsteps); % t0 = 0; tf = 10, nsteps = 100;

Since these files do not ship with MATLAB, these solvers are not officially supported.

Best Answer

Related Solutions

MATLAB: Ode45 : order, number of prediction and step time (theory)

MATLAB: Is there a fixed-step Ordinary Differential Equation (ODE) solver in MATLAB 8.0 (R2012b)

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