MATLAB Find the max point from a dsolve formula

Question

I'm solving two differential equations and plotting the results of the second differential equation. I want to find the values at the max point in the plot. However, maybe because I'm using sym, I'm having trouble figuring how to do it. I know that in math, you would just find the first derivative and set it to zero.

% Constants
k1 = 1/10; 
k2 = 1/1.3; 
k3 = 1/1.3; 
k4 = 1/(1/48);
k5 = 1/3.9; 
t = 1:5;
% Initial concentration
A0 = 5891.694;
B0 = 0; 
%%% Mass balance equation 1
syms A(t) t
eqn = diff(A,t) == -k1*A -k2*A -k3*A -k4*A;
cond = A(0) == A0;
A(t) = dsolve(eqn,cond);
% A(t) = exp(-k1*t);
%%% Mass balance equation 2
syms B(t) t
eqn = diff(B,t) == k1*A +k2*A +k3*A +k4*A - k5*B;
cond = B(0) == B0;
B(t) = dsolve(eqn,cond); 

%%% Plot
figure('visible','on');
t = 0:20;
plot(t,B(t)) 

So for the picture above, I'd like to find the max point. Sometimes, it isn't at exact time steps so I want MATLAB to just show the exact values at the max point.

Answer 1

You can use findpeaks to find maxima in your data. To do so, first you need to convert your ode solution (algebraic expression) into a data list for a specific interval of study.

B(t) = dsolve(eqn,cond,'t') ;
t = 0:0.1:20;
z=eval(B(t))

Now using findpeaks

[pks, locs] = findpeaks(z)

pks =

5.7310e+03

locs =

 2