Question

Find the root of f(x) = ex- a. Using incremental search method. b. Using bisection method. c. Compare the processing time of two methods for error of less than 0.01%. d. Compare the error for 20 iterations between the two methods.

Answer 1

Given

$f(x)=e^x-3x$

1)

%incremental search method
f=@(x) exp(x)-3*x;
x0=0;
dx=0.1;
while f(x0+dx)>1e-4
while (f(x0)*f(x0+dx))>0
x0=x0+dx;
end
dx=dx.*0.1;
end
disp(['root of the equation to desired accuracy is x = ' num2str(x0)]);

--------------------------------------------------------

>> m1
root of the equation to desired accuracy is x = 0.619
>>

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2)bisection method

$f(x)=e^x-3x$

f(0)=1>0
f(1)=e-3=-0.282<0

therefore

root lies between x=0 and x=1

-------------------------

%bisection method
f=@(x) exp(x)-3*x;
x1=0;
x0=1;
x2=0.5*(x1+x0);
while abs(f(x2))>1e-4;
if f(x2)<0
x0=x2;
else
x1=x2;
end
x2=0.5*(x0+x1);
end
disp(['root of the equation to desired accuracy is x = ' num2str(x2)]);

---------------------------------

>> m4
root of the equation to desired accuracy is x = 0.61914
>>

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