Matlab實現——Recursive Trapezoidal Rule

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rctrap.m

%Program 7.3 (Recursive Trapezoidal Rule).

function T=rctrap(f,a,b,n,tol)

%Input    - f is the integrand input as a string ’f’

%   - a and b are upper and lower limits of integration

%   - n is the number of times for recursion

%   -tol is the tolerance

%Output  - T is the recursive trapezoidal rule list

M=1;

h=b-a;

T=zeros(1,n+1);

T(1)=h*(feval(f,a)+feval(f,b))/2;

err=1;

while(err>tol)

    for j=1:n

         M=2*M;

         h=h/2;

         s=0;

         for k=1:M/2

            x=a+h*(2*k-1);

            s=s+feval(f,x);

         end

         T(j+1)=T(j)/2+h*s;

         err=abs(T(j)-T(j+1));

    end

end

fun.m

 

function f=fun(x)

f=2*x-x.^2;

 

 

 

untitled.m

 

a=0;

b=2;

n=20;

tol=5*10e-6;

f='fun';

T=rctrap(f,a,b,n,tol)

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