I need some help adjusting my system of differential equations code.

I'm having some issues in regards to my code. Currently, this is the code:

l0 = 3; % initial length of plant
w0 = 0; % initial amount of water
n0 = 0; % initial amount of nutrients in dirt
S = 1; % the sun
a = 1;
b = 1;
e = 1; % evaporation
tr = [0 100]; % time from 0 to 10 
var0 = [w0, l0, n0, S]; % variables
[tt, xx] = ode45(@(t, x) first_order(x, t, a, b, e), tr, var0); % ode45's set up
w = xx(:,1); % this is w0
n = xx(:,2); % this is n0
L = xx(:,3); % this is l0
S = xx(:,4); % this is S (sun)

if t < 5 
    Rdash = Val; % step function value (1 in case of unit step function)
else 
    Rdash = 0;
end

function dLdt = first_order(t, l, a, b, e)
    dLdt = zeros(size(l));
    C = 1;
    R = 1;
    dLdt(1) = e+ b.*l(3) + C.*R;
    dLdt(2) = a.*l(3);
    dLdt(3) = a.*(l(4)+l(1)+l(2))*(2-1/k);
    dLdt(4) = dLdt(3);
end

And these are the errors:

>> odecodeforclass

Index exceeds matrix dimensions.

Error in odecodeforclass>first_order (line 20)

dLdt(1) = e+ b.*l(3) + C.*R;

Error in odecodeforclass>@(t,x)first_order(x,t,a,b,e)

Error in odearguments (line 90)

f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in odecodeforclass (line 10)

[tt, xx] = ode45(@(t, x) first_order(x, t, a, b, e), tr, var0); % ode45's set up

>>

I added some commentary to help. For context, I'm coding this differential system here:

dL/dt = aL(L0 - Lf) where L'=a(S+W+N)(1-1/k)

S = dL where d is constant

W' = E + bL + cR

N' = aL

where E = evaporation, R = rain water, and R'=0 is a step function

[4:29 PM]

S = sun, W = water, N = nutrients

[Torsten]

1. function dLdt = first_order(l,t,a,b,e)
2. k is undefined in first_order
3. Make sure that dLdt is a column vector.

Answer 1

[Sulaymon Eshkabilov]

Hi,

There are a couple of crucial points overlooked in your code:

l0 = 3; % initial length of plant
w0 = 0; % initial amount of water
n0 = 0; % initial amount of nutrients in dirt
S = 1; % the sun
a = 1;
b = 1;
e = 1; % evaporation
tr = linspace(0, 10); % time from 0 to 10 
var0 = [w0, l0, n0, S]; % variables
% NB: wrong order of your variables t and x
[tt, xx] = ode45(@(t, x) first_order(t, x, a, b, e), tr, var0); % ode45's set up
w = xx(:,1); % this is w0
n = xx(:,2); % this is n0
L = xx(:,3); % this is l0
S = xx(:,4); % this is S (sun)
plot(tt,xx)
if tt < 5 
    Rdash = Val; % step function value (1 in case of unit step function)
else 
    Rdash = 0;
end

function dLdt = first_order(t, l, a, b, e)
    dLdt = zeros(size(l));
    C = 1;
    R = 1;
    k = 1;   % Was not defined. Insert the right value
    dLdt(1) = e+ b.*l(3) + C.*R;
    dLdt(2) = a.*l(3);
    dLdt(3) = a.*(l(4)+l(1)+l(2))*(2-1/k);
    dLdt(4) = dLdt(3);
end

Good luck.