Using for loop for midpoint method

Hi guys, this is my code

m = 1000;
f = 75000;
v0 = 0;
h = 0.1;
tspan = [0 10];
c = [50,100,500,1000,2000];
dvdt = cell(1,length(c));
for i = 1:length(c);
    dvdt{i} = @(t,v) (f-c{i}*v)/m;
end
t =cell(1,length(c));
v =cell(1,length(c));
for k = 1:length(c)
    [t{k},v{k}]=midpoint(dvdt{1,k},tspan,v0,h)
end

Error using midpoint
Too many output arguments.

%% Question 

I want to use midpoint to calculate the t and v, and my dvdt is relied on c(constant values run from 50 to 2000). The code works, but t and v are released just only based on c = 50, which means my for loop does not work. Can someone please help !!!

Thanks in advance

Answer 1

[Hitesh]

Hi Khang,

The error "Too many output arguments" indicates that the "midpoint" function did not return two outputs. You need to initializes time and velocity vectors and applies the midpoint method to solve the differential equation. Kindly refer to the folllowing revised code for better understanding:

function [t, v] = midpoint(dvdt, tspan, v0, h)
    % Initialize time and solution vectors
    t = tspan(1):h:tspan(2);
    v = zeros(size(t));
    v(1) = v0;
    
    % Midpoint method loop
    for n = 1:(length(t) - 1)
        tn = t(n);
        vn = v(n);
        k1 = h * dvdt(tn, vn);
        k2 = h * dvdt(tn + h/2, vn + k1/2);
        v(n+1) = vn + k2;
    end
end

m = 1000;
f = 75000;
v0 = 0;
h = 0.1;
tspan = [0 10];
c = [50, 100, 500, 1000, 2000];
dvdt = cell(1, length(c));

% Create the differential equations for each value of c
for i = 1:length(c)
    dvdt{i} = @(t, v) (f - c(i) * v) / m;
end

t = cell(1, length(c));
v = cell(1, length(c));

% Solve using the midpoint method for each value of c
for k = 1:length(c)
    [t{k}, v{k}] = midpoint(dvdt{k}, tspan, v0, h);
end