MATLAB:Ordinary Differential Equations/Examples

The following examples show different ways of setting up and solving initial value problems in MATLAB. It is part of the page on Ordinary Differential Equations in MATLAB.

Examples

Note - each example began with the Templates provided at this web site. Some comments have been removed from the templates to conserve space while some comments may have been added to provide a clearer explanation of the process for a particular example.

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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