corrected trapezoid rule function code

Question

PetronasAMG 2017-12-3

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/370800-corrected-trapezoid-rule-function-code

评论： Jan 2018-2-4

I need help on matlab coding!!

so assignment given is to use trapezoid rule, midpoint rule and corrected trapezoid rule to plot log vs log error plot here is what i have so far

This is the main script function:

a = 0;

b = 2;

%take the integral of the given function

Int = exp(2^2-1)- exp(0^2-1);

%preallocate the estimates and errors

trap_value = zeros(1,12);

mid_value = zeros(1,12);

correctedtrap_value = zeros(1,12);

trap_error = zeros(1,12);

mid_error = zeros(1,12);

correctedtrap_error = zeros(1,12);

%number of steps given in the problem (n)

k = 1:1:12;

n = 2.^k;

%repeat the value of n

for j = 1:12

trap_value(j) = traprule(a,b,n(j));

mid_value (j) = midpoint(a,b,n(j));

correctedtrap_value (j) = correctedtrapezoid (a,b,n(j));

trap_error(j) = abs(Int-trap_value(j));

mid_error = abs(Int-mid_value(j));

correctedtrap_error = abs(Int-correctedtrap_value(j));

end

figure(1)

plot(log(n),log(trap_error),log(n),log(mid_error),log(n),log(correctedtrap_error))

legend('Three rules estimate log(error) vs log(number of steps)','Location','best')

xlabel('log(n)')

ylabel('log(error)')

This is the given function to evaluate:

function [f] = func_main(x)

%this function will calculate 2xexp(x^2-1) and given x

f = 2*x*exp(x^2-1);

end

This is the trapeziod rule:

function [I] = traprule(a,b,n)

%Function called: func_main

%initiate the value for h

h = (b-a)/n;

%preallocate the output

I = 0;

for j=1:n

%left point of j trapezoid

left = a+h*(j-1);

%right point of trapezoid

right = a+h*j;

%apply the main fucntion

fleft = func_main(left);

fright = func_main(right);

%size the j trapezoid

trap = (fleft+fright)*h/2;

%add to continue the estimate

I = I+trap;

end

HERE IS WHERE I NEED YOUR HELP!!!!!!

so given the equation of CORRECTED TRAPEZOID RULE equation, I have to use equation to get proper value for corrected trapezoid rule.(which is attached a picture)

so Tn(f), I am guessing is the value i got from trapezoid rule function, where i already made the function file for, now i need to code to get T^c n (f). Only problem is that I am really struggling how to start the function file for CORRECTED TRAPEZOID RULE. Please help me how to write corrected trapezoid rule that can link up to the main script so i can plot out the log graph! the detail and sample coding will be a great help!