Question

Question 25 2 pts MATLAB's fminbnd function can be used to find the minimum value of a function of two independent variables. True False Question 26 5 pts Given the boundary value problem: du du dza w(x = 1) = 5 wx = 10) = 5 =W 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 -15.33 -0.55 10.25

Answer 1

25. FALSE , as fminbnd finds the minimum of a function of one variable within a fixed interval, anad will find a minimum that occurs on a boundary. to find more than one variable, we use fminsearch function.

26.ANSWER : (a) 0.55 (minimum value of w)

MATLAB CODE : ( by shooting method)

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