plot (error) grid on; title(\'Plot of error\'); xlabel(\'iterations\'); ylabel(\

Question

plot (error)

grid on;

title('Plot of error');

xlabel('iterations');

ylabel('Error');

Modified Regula Falsi Method Frequently, in the regula falsi method, one of the endpoints of the interval stays the same in all iterations, while the other endpoint advances toward the root (Fig.1). In the modified regula falsi method, when this situation occurs, the straight line that connects the endpoints of the interval is replaced with a line that has a smaller slope. As shown in Fig.2, this is done by dividing by 2 the value of the function at the end point that stays the same. Consequently, the line intersects the x-axis closer to the root. f(x)t Abi) NS2 Actual62 solution Ka) Figure 1: Regula Falsi method

Explanation / Answer

function ModRegFal = ModRegFal(a, b, n)
format long;
a = input('Enter a value for lower boundary a: ');
b = input('Enter a value for upper boundary b: ');
n = input('How small should should the error be (to what -power)? ');
if (f(a)*f(b) > 0 )
disp ('Invalid values of a and b. Program Closing')
return;
end;
F = f(a);
G = f(b);
w0 = a;
while (1)
wn = (G*a-F*b)/(G-F);
disp([a b wn w0]) %% just checking where the values are, and it they look correct
if f(a)*f(wn) > 0
disp('ranif 1')%% just checking where the values are, and it they look correct
b = wn;
G = f(wn);
if f(w0)*f(wn) > 0
F = F/ 2; end;
disp('ranif 2')%% just checking where the values are, and it they look correct
disp([a b wn w0])%% just checking where the values are, and it they look correct
else
a = wn;
F = f(wn);
if f(w0)*f(wn) > 0
disp('ranif 3')%% just checking where the values are, and it they look correct
disp([a b wn w0])%% just checking where the values are, and it they look correct
G = G/ 2; end;
end
disp([a b wn w0])
if (abs((wn - w0)/wn) < 0.5*10^-n)
disp ('The root is: ')
disp (wn)
break;
else
w0 = wn;
end
plot (error)
grid on;
title('Plot of error');
xlabel('iterations');
ylabel('Error');

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