Numerical equation intergral.

Hi,

I have an equation

a = 0.8

b = 45°

x = ((((1-(a^2))^0.5)*((x/z)+(z/x))*((a*tan(b)) - 1 + ((1-(z/x))^2.25)))^-1); (eq 1)

the above function can only be solved numerically. I used the fimplicit function and I was sucessful in plotting the x Vs. y graph. Now I would like to find t, where

t = integral (f(x,y)) dy

for example you can take f(x,y) = y*exp((x-y*y-xy)*x). Since x and y are related and the equation 1 can be solved only numerically, I am not able to find a solution. Can you help me in solving the equation please ?

[Torsten]

Call integral as

I = integral@fun,ymin,ymax,'ArrayValued',true);

and write a function fun as

function f = fun(y)

function_implicit = @(x) (the function that you solved using fimplicit with z replaced by y)

x0 = 1;

x = fzero(function_implicit,x0);

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

end

[Venkatesh Pandian narayanasamy]

Hey,

Thanks a lot for your support and I tried the following code.

syms y

I = integral(fun,0.1,1,'ArrayValued',true);

function f = fun(y)

a = 0.8;

b = 45;

function_implicit = @(x) (x-((((1-(a^2))^0.5)*((x/y)+(y/x))*((a*tan(b)) - 1 + ((1-(y/x))^2.25)))^-1));

x0 = 1;

x = fzero(function_implicit,x0);

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

end

but I recieve the following error from MATLAB stating that

Error using fzero>localFirstFcnEval (line 729)

FZERO cannot continue because user-supplied function_handle ==> @(x)(x-((((1-(a^2))^0.5)*((x/y)+(y/x))*((a*tan(b))-1+((1-(y/x))^2.25)))^-1)) failed with the error below.

Unrecognized function or variable 'y'.

Error in fzero (line 286)

fx = localFirstFcnEval(FunFcn,FunFcnIn,x,varargin{:});

Error in hg>fun (line 8)

x = fzero(function_implicit,x0);

Error in hg (line 2)

I = integral(fun,0.1,1,'ArrayValued',true);

[Torsten]

Remove the line

syms y

And for b in degrees you have to use the tand function, not tan.

[Venkatesh Pandian narayanasamy]

I still recieve the foloowing error unfortunately.

Error using fzero>localFirstFcnEval (line 729)

FZERO cannot continue because user-supplied function_handle ==> @(x)(x-((((1-(a^2))^0.5)*((x/y)+(y/x))*((a*tand(b))-1+((1-(y/x))^2.25)))^-1)) failed with the error below.

Unrecognized function or variable 'y'.

Error in fzero (line 286)

fx = localFirstFcnEval(FunFcn,FunFcnIn,x,varargin{:});

Error in awas>fun (line 8)

x = fzero(function_implicit,x0);

Error in awas (line 2)

I = integral(fun,0.1,1,'ArrayValued',true);

[Torsten]

Try

function f = fun(y0)

y = y0;

% everything else the same, starting from line a = 0.8;

[Venkatesh Pandian narayanasamy]

I recive unfortunately the following error. Thanks a lot man for your support :)

Not enough input arguments.

Error in hgkj>fun (line 3)

y = y0;

Error in hgkj (line 1)

I = integral(fun,0.1,1,'ArrayValued',true);

[Torsten]

I wrote

I = integral(@fun,...

not

I = integral(fun,...

[Venkatesh Pandian narayanasamy]

okay. It's working now, but I recieve the following output. I think it's because equation 1 can only be solved numerically and it doesn't have finite solutions.

Exiting fzero: aborting search for an interval containing a sign change

because complex function value encountered during search.

(Function value at 0.0971721 is -1.0233+2.8867e-05i.)

[Torsten]

Could you include a z-x plot for your function for 0.1<=z<=1 ?

[Venkatesh Pandian narayanasamy]

Here you see the plot. Consider Y = Z.

[Torsten]

Then try

x0 = 2*y0;

instead of

x0 = 1.0;

Just to be sure: The z in your equation is the y with respect to which you are integrating ?

And please include the code you are using at the moment.

[Torsten]

I tried Mathematica under wolframalpha.com in the internet using the ContourPlot command.

It appears, given y in the relevant range, there are multiple solutions for your equation for x.