ODE graph for multiple occurrences

Hello,

My MATLAB code as of right now will graph a ODE for one value of gamma. I would like to write the code so that it graphs 8 plots all on the same graph for varrying values of gamma. Values of gamma will be 0 through 2 with a step of .25. Here is my code currently:

tspan = [0 50];

y0 = [2 0]';

[t,y] = ode45(@hw1,tspan,y0);

plot(t,y(:,1))

function dy = hw1(t,y)

gamma = 1

dy(1)= y(2);

dy(2)= -gamma*y(2)-y(1);

dy = [dy(1);dy(2)];

title('Gamma equals .25')

end

Thank yoU!

Answer 1

[Star Strider]

Define the γ vector (‘gammav’ here), use a loop, and see the documentation section on Passing Extra Parameters.

tspan = [0 50];
y0 = [2 0]';
gammav = logspace(-1, 1, 5)

gammav = 1×5

0.1000 0.3162 1.0000 3.1623 10.0000

for k = 1:numel(gammav)
    [t{k},y{k}] = ode45(@(t,y)hw1(t,y,gammav(k)),tspan,y0);
end

figure
hold on
for k = 1:numel(gammav)
    plot(t{k},y{k}(:,1))
end
grid
legend(compose('$\\gamma = %.2f$',gammav), 'Location','best', 'Interpreter','latex')

    function dy = hw1(t,y,gamma)
    dy(1)= y(2);
    dy(2)= -gamma*y(2)-y(1);
    dy = [dy(1);dy(2)];
    end

.