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

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MathWorks Support Team on 13 Dec 2012
Commented: Bandar on 28 Jul 2021
All the current ODE solvers are variable-step. I would like to use a fixed-step solver.

MathWorks Support Team on 29 Aug 2019
Edited: MathWorks Support Team on 29 Aug 2019
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.
Bandar on 28 Jul 2021
Can you show how to use this fixed solver step by step? It seems it requires tspan as a vector but I need it as scalar so I can animate the solution. Is this even possible?

Deepraj on 27 Jan 2014
Why does the ODE is being executed twice at t0 ? This is causing problem in my code. I found this by displaying 't' in the file where differential equations are written.

Shivam on 20 Mar 2014
Hi Deepraj, I got around the problem by just taking the second row at that particular instance. Infact the ode4 method executes twice at each fixed time step, so each time I get the 2nd row.

R14SP1

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