MATLAB: Ode45 is returning the incorrect solution

differentiationintegrationMATLABode45too large

I am running an ode45 to solve a simple intergration. The intergration is so simple I can perform it by hand – hence knowing the solution returned is excessively large.

function [Output] = ContinuousFeed(t,u)

uA = u(1);

uB = u(2);

uE = u(3);

uF = u(4);

u = [uA; uB; uE; uF];

Output = u;

end

t=[0 10];

u0 = [1; 0.0002; 0; 0];

[t, u] = ode45 (@ContinuousFeed, t ,u0);

Why is it returning a final value of 22030.53 for the first column? All other columns are displaying inaccurate answers also.

Thank you!

Best Answer

The MATLAB is giving the correct solution. You are solving four independent ODEs of the form

which have an anatylical solution

The solution of ode45 matches this analytical solution.

Related Solutions

MATLAB: Solving 2nd order nonlinear ode Numeric solution by using ode45

This is the basic structure for solving the ode.

u0 = 2;
v0 = 0;
tspan = [0 5];
k = 1;
a = 25;
[t,U] = ode45(@odefn, tspan, [u0 v0],[],k,a);
u = U(:,1);
v = U(:,2);
plot(t,u),grid
xlabel('t'),ylabel('u')
function dUdt = odefn(~,U,k,a)
        u = U(1);
        v = U(2);   % v = du/dt
        dvdt = k*(1-u^2)*v - a*u;
        
        dUdt = [v;
                dvdt];
end

You could investigate fzero to get the value of k that gives 1.25 beats/sec, or adjust it manually (as I did here to get an approximate value).

MATLAB: Solving FitzHugh-Nagumo equations using ODE45

Here is my achievement. I don't get about stim. Can you explain more?

%             du/dt = c1u ( u  − a)(1 − u) − c2uv +stim
%             dv/ dt  = b (u  − v)  
a = 0.13;
b = 0.013;
c1 = 0.26;
c2 = 0.1;
% let y(1) = u; y(2) = v
F = @(t,y)  [c1*y(1)*(y(1)-a)*(1-y(1)-c2*y(1)*y(2)+stim)
            b*(y(1)-y(2))];
tspan = [0 2];              % time
y0 = [1 2];                 % u0 = 1; v0 = 2;
[t,y] = ode45(F,tspan,y0);
plot(t,y)
legend('u(t)','v(t)')

Best Answer

Related Solutions

MATLAB: Solving 2nd order nonlinear ode Numeric solution by using ode45

MATLAB: Solving FitzHugh-Nagumo equations using ODE45

Related Question