Question

Write a MATLAB function/script that performs the following tasks. Approximate: 2+2 (a) Using the composite Trapezoidal rule with n=8 (b) Using the composite Simpson's rule with n = 8 (c) Display the final solution for each method along with the exact solution. Name your file: WS5_LastName_First Inital()

Answer 1

a)

function t=comptraprule(f,a,b,n)
h=(b-a)/n;
exactVal=log(b^2+2)-log(a^2+2);
sum=0;
for i=1:n-1
x(i)=a+i*h;
sum=sum+f(x(i));
end
Itrap=h*(f(a)+2*sum+f(b))/2;
disp(['Itrap:'' ',num2str(Itrap)]);
disp(['exactVal:'' ',num2str(exactVal)]);
end

b)

function s=simprl(f,a,b,n)
h=(b-a)/(2*n);
exactVal=log(b^2+2)-log(a^2+2);
s1=0;
s2=0;
for k=1:n
x=a+h*(2*k-1);
s1=s1+f(x);
end
for k=1:(n-1)
x=a+h*2*k;
s2=s2+f(x);
end
Isimp=h*(f(a)+f(b)+4*s1+2*s2)/3;
disp(['Isimp:'' ',num2str(Isimp)]);
disp(['exactVal:'' ',num2str(exactVal)]);
end

c) After saving both the above codes in the script window as (comptraprule.m) and simprl.m respectively (don't rule) and type the below code:

>> simprl (@(x) (2*x)/(x^2+2), 0,4,8) Isimp:' 2.1973 exactVal:' 2.1972 >> comptraprule (@(x) (2*x)/(x^2+2), 0,4,8) Itrap:' 2.1743 exactval:' 2.1972