Shooting Method with Secant Method

Hi all,
I am working on a problem to solve a second order differential equation. I am using the numerical method ‘the shooting method’ and I need to perform iterations to find the initial value of the slope. To do this I am using the secant method. My intial values to start the shooting method for z are -4 and 4. From this is get the corresponding y values of -65.025 (3dp) and 106.062 (3dp) respectively. I am aiming to find the value of z when y = 0. Thus, I proceed to the secant method to find the value of ‘z’ when y = 0;
The formula for secant method is:
z2 = z1 – (y(z1) – 0)*(z1 – z2)/(y(z1 – y(z0))
I want to make a loop where this updates: Hence:
z0 = z1
z1 = z2
y(z0) = y(z1)
y(z1) = y(z2)
So, the next iteration is:
z3 = z2 – (y(z2) – 0)*(z2 – z21/(y(z2 – y(z2))
The thing is I now need to compute y(z2). I can do this, but it would meaning copying and pasting another block of code. Thus, my question is how to make the algorithm in MATLAB so that I can perform the desired number of iterations I want within the for loop? Rather than copying and pasting the code below over and over again until I reach a satisfactory point of convergence?

Here is my code:
clear, clc, close all

format longG

% Structural Properties
E = 2.1E+08;
Ic = 22530/100^4;
Ib = 19460/100^4;
Ac = 168/100^2;
h = 0.5;
r = 1;
Gi = (1*E*Ib/10);
Ci = 1/2*(E*Ic/h);
g = Gi/Ci;
K = (6*g + 1 + r);
V = [0 0 0 0 0 35 0 0 0 0 0 25 0 0 0 0 0 15 0 0 0 0 0 5 0];

%Initial Conditions 1
y = 0
z = -4
for i = 1:24
if i == 6 || i == 12 || i == 18
F(i) = h*(V(i) + V(i+6))/(4*Ci);
z(i+1) = z(i) + ((F(i) – K*z(i) + y(i))/(-z(i)))*h;
y(i+1) = y(i) + z(i)*h;
else F(i) = 0;
z(i+1) = z(i) + ((F(i) – K*z(i) + y(i))/(-z(i)))*h;
y(i+1) = y(i) + z(i)*h;
end
if i == 24
F(i) = h*(V(i))/(4*Ci);
z(i+1) = z(i) + ((F(i) – K*z(i) + y(i))/(-z(i)))*h;
y(i+1) = y(i) + z(i)*h
end
q0 = y(end)
p0 = z(1)
end
q0 = y(end)
p0 = z(1)

%Initial Conditions 2
y = 0
z = 4
for i = 1:24
if i == 6 || i == 12 || i == 18
F(i) = h*(V(i) + V(i+6))/(4*Ci);
z(i+1) = z(i) + ((F(i) – K*z(i) + y(i))/(-z(i)))*h;
y(i+1) = y(i) + z(i)*h;
else F(i) = 0;
z(i+1) = z(i) + ((F(i) – K*z(i) + y(i))/(-z(i)))*h;
y(i+1) = y(i) + z(i)*h;
end
if i == 24
F(i) = h*(V(i))/(4*Ci);
z(i+1) = z(i) + ((F(i) – K*z(i) + y(i))/(-z(i)))*h;
y(i+1) = y(i) + z(i)*h
end
end
q1 = y(end)
p1 = z(1)

% Secant Method

p2 = p1 – (q1 – 0)*(p1 – p0)/(q1 -q0)

I have left the secant method formula outside the loop, because I am unsure how to include it in the loop to perform the iterations I previously explained.
I understand that this is quite a long question. So thank you in advance for any help. However, you guys on here are great, so I hoping its not too tedious for you.
Many thanks,
ScottHi all,
I am working on a problem to solve a second order differential equation. I am using the numerical method ‘the shooting method’ and I need to perform iterations to find the initial value of the slope. To do this I am using the secant method. My intial values to start the shooting method for z are -4 and 4. From this is get the corresponding y values of -65.025 (3dp) and 106.062 (3dp) respectively. I am aiming to find the value of z when y = 0. Thus, I proceed to the secant method to find the value of ‘z’ when y = 0;
The formula for secant method is:
z2 = z1 – (y(z1) – 0)*(z1 – z2)/(y(z1 – y(z0))
I want to make a loop where this updates: Hence:
z0 = z1
z1 = z2
y(z0) = y(z1)
y(z1) = y(z2)
So, the next iteration is:
z3 = z2 – (y(z2) – 0)*(z2 – z21/(y(z2 – y(z2))
The thing is I now need to compute y(z2). I can do this, but it would meaning copying and pasting another block of code. Thus, my question is how to make the algorithm in MATLAB so that I can perform the desired number of iterations I want within the for loop? Rather than copying and pasting the code below over and over again until I reach a satisfactory point of convergence?

Here is my code:
clear, clc, close all

format longG

% Secant Method

p2 = p1 – (q1 – 0)*(p1 – p0)/(q1 -q0)

I have left the secant method formula outside the loop, because I am unsure how to include it in the loop to perform the iterations I previously explained.
I understand that this is quite a long question. So thank you in advance for any help. However, you guys on here are great, so I hoping its not too tedious for you.
Many thanks,
Scott Hi all,
I am working on a problem to solve a second order differential equation. I am using the numerical method ‘the shooting method’ and I need to perform iterations to find the initial value of the slope. To do this I am using the secant method. My intial values to start the shooting method for z are -4 and 4. From this is get the corresponding y values of -65.025 (3dp) and 106.062 (3dp) respectively. I am aiming to find the value of z when y = 0. Thus, I proceed to the secant method to find the value of ‘z’ when y = 0;
The formula for secant method is:
z2 = z1 – (y(z1) – 0)*(z1 – z2)/(y(z1 – y(z0))
I want to make a loop where this updates: Hence:
z0 = z1
z1 = z2
y(z0) = y(z1)
y(z1) = y(z2)
So, the next iteration is:
z3 = z2 – (y(z2) – 0)*(z2 – z21/(y(z2 – y(z2))
The thing is I now need to compute y(z2). I can do this, but it would meaning copying and pasting another block of code. Thus, my question is how to make the algorithm in MATLAB so that I can perform the desired number of iterations I want within the for loop? Rather than copying and pasting the code below over and over again until I reach a satisfactory point of convergence?

Here is my code:
clear, clc, close all

format longG

% Secant Method

p2 = p1 – (q1 – 0)*(p1 – p0)/(q1 -q0)

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