MATLAB Mathematics - SERC - Index of

Initial Value Problems for ODEs and DAEs
In this example, the first call to ode45 uses the defaults for the solver
parameters:
ode = @(t,y) abs(y);
[t0,y0] = ode45(ode,[0, 40], 1);
The second uses options to impose nonnegativity conditions:
options = odeset('NonNegative',1);
[t1,y1] = ode45(ode,[0, 40], 1, options);
This plot compares the numerical solution to the exact solution.
Here is a more complete view of the code used to obtain this plot:
ode = @(t,y) abs(y);
options = odeset('Refine',1);
[t0,y0] = ode45(ode,[0, 40], 1,options);
options = odeset(options,'NonNegative',1);
[t1,y1] = ode45(ode,[0, 40], 1, options);
t = linspace(0,40,1000);
y = exp(-t);
plot(t,y,'b-',t0,y0,'ro',t1,y1,'b*');
legend('Exact solution','No constraints','Nonnegativity', ...
'Location','SouthWest')
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