Iteration of two equations with two unknowns

Hello, I have these two equations: where R0 and V0 are the known initial values with the range of t given.

V1=(A/R0)*(t1-t0) + V0

and

R1=V0*(t1-t0) + R0.

The second iteration will be in the form of

V2=(A/R1)*(t2-t1) + V1

and

   R2=V1*(t2-t1) + R1 etc...

My challenge is that I want the iteration to terminate at a particular value R which I don't know how to incorporate into a 'for loop' code. Kindly assist.

Answer 1

[Walter Roberson]

You do not use a "for" loop for something like that. You use a "while" loop.

while( abs(R(end) - target_R) > tolerance
  ...
end

However, it is safer to put an upper limit on the iterations in case there is no convergence:

for iter = 1 : 1000
  ...
  if abs(R(end) - target_R) <= tolerance; break; end
end

[Shozeal]

Thank you, Walter.

Maybe I should type in the code I have written here as I am still not getting the expected result. I will assume values for each known variable.

t_final = 10;
t_delta=t_final/N
A = 200 ;
n = 0;
V_0 = 2e4;
R_0 = 0.2:20:2e4;
hold on
while n<length (R_0)
n = n+1
if k(1)==1
V(k)=V_0
R(k)=R_0
end
for k=1:N;
V(k+1)=(A/R(k))*t_delta+V(k);
R(k+1)=V(k)*t_delta+R(k);
end
hold on
plot(t_delta,R)
end
hold off
R
V

Based on what I wrote up here, I did not get anything reasonable.

Thanks.

[Walter Roberson]

What is N ?

[Walter Roberson]

I do not know what you are trying to do. Maybe something like

N = 100;
t_final = 10;
t_delta = t_final/N;
A = 200 ;
n = 0;
V_0 = 2e4;
R_0 = 0.2;
V=V_0;
R=R_0;
times = linspace(0,t_final,N+1);

for k=1:N
  V(k+1)=(A/R(k))*t_delta+V(k);
  R(k+1)=V(k)*t_delta+R(k);
end

plot(times,R)

hold off
disp(R(end))
disp(V(end))

[Shozeal]

This is so perfect, I really appreciate. I only needed to add the 'while' statement to accommodate my vector values for R and t.

Thanks a lot.

Answer 2

[Shozeal]

N = 100;

Answer 3

[Shozeal]

I have attached a copy of what I am trying to achieve.

Thanks for the guidance.

[Walter Roberson]

The code I posted should do that.

The V values become close to constant in just a few iterations, so the R ends up looking indistinguishable from linear.

It looks V is an acceleration of some sort and R is a velocity.

Answer 4

[Shozeal]

V is the velocity while R is like a position... displacement kind of.

Thanks, I believe what you sent earlier should do that.