Numeircal integral with external function and external parameter

Question

Saeid 2019-1-12

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/439478-numeircal-integral-with-external-function-and-external-parameter

编辑： Saeid 2019-1-13

I would like to calculate an integral whereas the integrand is a separate external function. Consider as an example that I have in my main script:

N=5; 
I = integral(fn,0,Inf,'RelTol',1e-8,'AbsTol',1e-13)

Where N is a parameter of the integrand that appears in the separate function named: fn.m that has the following form:

function FUN= fn(x)
	FUN=@(x) (x.^N).*exp(-x).*sin(x)
 end

But when I do this I see the following error:

Undefined function or variable 'N'.

How can I help Matlab take this external parameter into the integrand function?

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Answer 1

madhan ravi 2019-1-12

3
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/439478-numeircal-integral-with-external-function-and-external-parameter#answer_356125

编辑：madhan ravi 2019-1-12

EDITED

Parameterize function

N = 5; 
F = fn(x,N); % function call
I = integral(F,0,Inf,'RelTol',1e-8,'AbsTol',1e-13) 
function FUN = fn(x,N) % function definition
	FUN = @(x) (x.^N).*exp(-x).*sin(x);
end

Gives:

I =
  -15.0000

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Saeid 2019-1-13

Hi Madhan,

now that the method works I need to use these integrals in an fsolve routine to determine some coefficients. Are you familiar with the fsolve? If yes here is my problem: I would like to solve e.g. 2 equations in terms of itegrals (see below) to obtain two coefficients x1 & x2. If I write the program like this

clc
clear all
format long g
x0=[0 0]
x=fsolve(@FF4,x0)
function f4=FF4(x)
    f4(1)=integral(@(y) x(1)*y.^2+x(2)-2.3333,0,1)
    f4(2)=integral(@(y) x(1)*sin(x(2)*y),0,pi)     
end

It will work perfectly and gives me the factors x1=1 & x2=2.

Now if I try to define the integrals in separate functions just as you suggested previously (this time with two parameters: N from above is replaced by x1 & x2) again I will receive the error message

"Undefined function or variable 'y'."

The code now looks like this:

clc
clear all
format long g
x0=[0 0]
x=fsolve(@FF3,x0)
 
function f3=FF3(x)  
    f3(1)=integral(fint1(y,x(1),x(2)),0,1)-2.333
    f3(2)=integral(fint2(y,x(1),x(2)),0,pi)
end
function FUN1= fint1(y,x1,x2)
        FUN1=@(y) x1*y.^2+x2
end
function FUN2= fint2(y,x1,x2)
        FUN2=@(y) x1*sin(x2*y)
end

What am I doing wrong?

Walter Roberson 2019-1-13

function f3=FF3(x)  
    f3(1)=integral(fint1(x(1),x(2)),0,1)-2.333
    f3(2)=integral(fint2(x(1),x(2)),0,pi)
end
function FUN1= fint1(x1,x2)
        FUN1=@(y) x1*y.^2+x2
end
function FUN2= fint2(x1,x2)
        FUN2=@(y) x1*sin(x2*y)
end