MATLAB:Ordinary Differential Equations/Examples

The following examples show different ways of setting up and solving initial value problems in MATLAB.

Examples

Constant Rate of Change

If the dependent variable has a constant rate of change:

\( \begin{align} \frac{dy}{dt}=k \end{align} \)

where \(k\) is some constant, you can provide the differential equation with a function called ConstDiff.m that contains the code:

function dydt = ConstDiff(t, y, k)
% Differential equation for constant growth
% t is time
% y is the state vector
% k contains any required constants
% dydt must be a column vector
dydt = k(1); % or just k since there is only one

You could calculate answers using this model with the following code called RunConstDiff.m, which assumes there are 100 evenly spaced times between 0 and 10, the initial value of \(y\) is 6, and the rate of change is 1.2:

clear; format short e

% Set name of file containing derivatives
DiffFileName = 'ConstDiff';

% Set up time span, initial value(s), and constant(s)
% Note: Variables should be in columns
tspan = linspace(0, 10);
yinit = 6;
k = 1.2;

% Determine if states should be plotted
PlotStates = 1;

%% Under the hood
% Use ODE function of choice to get output times and states
DE = eval(sprintf('@(t, y, k) %s(t,y,k)', DiffFileName))
[tout, yout] = ode45(@(t,y) DE(t,y,k), tspan, yinit);

% Plot results
if PlotStates
    figure(1); clf
    StatePlotter(tout, yout)
end

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