Derivative of intergrated bessel function

Hi,

I'm trying to plot a curve determined by the first and second derivatives of an expression defined using besselj. The definitions of my derivatives and my function are below :

I've succeeded in defining the function as follow, using defined scalar for the integral :

Fhertz=@(r) P*l^2/(2*pi*D)*integral(@(m) besselj(0,m.*r/l).*m./(1+m.^4),0,1000)

But now I'm trapped as I can't find a way to calculate the 2 M as defined above, Matlab seems not to accept my function when I try to use the diff function :

Mr1= @(r)-D*(1/r*diff(Fhertz)+nu/r*diff(Fhertz,2))

fplot(Mr1, [0 10*l]);

Undefined function 'diff' for input arguments of type 'function_handle'.

Error in @(r)-D*(1/r*diff(Fhertz)+nu/r*diff(Fhertz,2))

Error in fplot>splitFunctionHandle (line 255) fnAtZero = fn(0);

Error in fplot (line 119) fn{1} = splitFunctionHandle(fn{1});

Thanks in advance for your help

Answer 1

[Steven Lord]

You can't do math on function handles. You can do math on the values returned by function handles.

s = @sin;
c = @cos;
tNO = @(x) s./c % will not work if you try to evaluate tNO
tYES = @(x) s(x)./c(x) % will work

v = -pi:0.1:pi;
tYES(v)-tan(v) % all elements should be small

See the example "Approximate Derivatives with diff" on the documentation page for diff for how to use it to approximate a function's derivative.

[Romain Clouzeau]

Thanks for the answer !

I've tried defining it as you suggested, but it doesn't work either. If I just define the function as depending on r I get :

Mr1= @(r)-D*(1/r.*diff(Fhertz(r))+nu./r*diff(Fhertz(r),2));
>> Mr1(8);
>> Mr1(8);
>> Mr1(8)
 ans =  []

So obviouvsly the function is not working.

If I try the method defined in the documentation pages, I can't even define the function :

 h = 0.001;       % step size
r = 0:h:10*l;    % domain
f = Fhertz(r);      % range
Y = diff(f)/h;   % first derivative
Z = diff(Y)/h;   % second derivative
A = @(r)-D*(1/r.*Y+nu./r*Z);
Matrix dimensions must agree.

 Error in @(m)besselj(0,m.*r/l).*m./(1+m.^4)

 Error in integralCalc/iterateScalarValued (line 314)
                fx = FUN(t);

 Error in integralCalc/vadapt (line 132)
            [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
      [q,errbnd] = vadapt(@AtoBInvTransform,interval);

 Error in integral (line 88)
Q = integralCalc(fun,a,b,opstruct);

 Error in @(r)P*l^2/(2*pi*D)*integral(@(m)besselj(0,m.*r/l).*m./(1+m.^4),0,1000)true

So I'm still stuck...

[Steven Lord]

If you call the diff function with a nonempty vector as input, the output vector has one fewer element than the input. You need to adjust for that.

Alternately, you may find the gradient function useful.