How can I define initial condition in a for loop?

Hi, I want to compute activity vectors vi from an initial activity v0 = [ 9 9] . I want to do it for time 0 to time 10 in steps of ∆t = 0.0001. At each iteration step, I have to compute vi+1 from vi as follows: vi+1 = vi + F (A · v + b) ∆t. The F is given as a function.

This is what I have done so far:

v_0= [9; 9];

T=10;

dt=0.0001;

v1=zeros(10000,2);

v=zeros(10000,2);

v1=v_0+Factivation(X, Rmax, k)*dt;

for i=1:10000*T

v(i+1,:)=v1(i,:)+Factivation(X, Rmax, k)*dt;

end

It doesn't seem correct. I do not know how to incoorporate the initial condition v(0) correctly and also I get this error:

Array indices must be positive integers or logical values.

Could you please help me?

Answer 1

[VBBV]

v_0= [9; 9];
T=10;
dt=0.0001; 
% define the time step in the time vector
K = 1:dt:T
v1=zeros(length(K)+1,3);
v=zeros(length(K)+1,3);

% take a transpose of v_0
v1=v_0.'+Factivation(X, Rmax, k)*dt;

% use in the for loop
for I=1:length(K)
    v(I+1,:)=v1(I,:)+Factivation(X, Rmax, k)*dt;
end

Answer 2

[Torsten]

syms x y(x)
Dy = diff(y);
sol = dsolve(diff(y,x,2)+y==0,y(0)==9,Dy(0)==9)

sol = 

v_0 = [9;9];
T = 10;
dt = 0.0001; 
N = T/dt;
v = zeros(N+1,2);
t = (0:dt:T).';
v(1,:) = v_0;
f = @(t,y) [y(2),-y(1)];   % Replace "f" by your function "Factivation". It must return a row vector of length 2
for i = 1:N
    v(i+1,:) = v(i,:) + dt*f(t(i),v(i,:));
end
hold on
plot(t,v)
plot(t,[9*(sin(t)+cos(t)),9*(cos(t)-sin(t))])
hold off