Question

matlab code

Given the boundary value problem: daw = W 3 dw dc2 de w(x = 1) = 5 w(x = 10) = 5 Find the minimum value of wover this region using the shooting method. Round your answer to TWO decimal points rounding up for 5 or more. 0.55 0 -15.33 -0.55 10.25

Answer 1

The detailed solution is given below.

d²w du? 3 do dn let, do % = f(z) dn dz du w-3t = f(w,z) Shooting Method an With = Wit care andi onl Will= wit f (Z;) eu Zit = Z; + on du Zih - Z; + tz (witz) on

clear;
clc;

% Shooting Method
f1 = @(z) z;
f2 = @(w,z) w - 3*z;

h = 0.001;
a = 1;
b = 10;

% Initialize
x = a:h:b;
n = numel(x);
w = zeros(1,numel(x));
w(1) = 5;
z = zeros(1,numel(x));
z(1) = -15.33;

for i=1:n-1
    w(i+1) = w(i) + f1(z(i))*h;
    z(i+1) = z(i) + f2(w(i),z(i))*h;
end
fprintf('Minimum Value of w=%.2f\n',round(min(w),2))

figure(1)
hold on
plot(b,5,'ko','MarkerFaceColor','k','DisplayName','Actual Value at x = 10')
plot(x,w,'r-','DisplayName','Shooting Method','linewidth',2)
legend show
xlabel('x')
ylabel('w')
grid on

5.5 5 Actual Value at x = 10 Shooting Method 4.5 4 3.5 3 3 2.5 2 1.5 1 0.5 1 2 3 4 5 6 7 8 9 10 X

Output

Minimum Value of w=0.55 >> |

Thus the first option is correct.

Please rate the solution if found satisfactory.