How to use fsolve an implicit equation?

clc, clear
a1=28*7*400;                        %%ft^2
po=40.6;                            %%psi
delpio=9;                           %%psi
qf=1525;                            %%gpm
qo=qf;
pp=16.4;                            %%psi
qp=1234;                            %%gpm
depr1=24.9;                         %%psi
delpr2=18.2;                        %%psi
PH=360;                                     %%ft
lp=2.76*.264/(60)^2*14.5;                   %%gal/m*min^2/psi
k2=1.75*10^-4*60^1.67*14.5/264.172^1.67;     %%psi/(gal/min)^1.67
k3=2.27*10^-2;                      %%(m^3/h)^.6/m^2
g=32.17;                            %%ft/s^2
rhoh20=62.4;                        %%lbs/ft^3
pf=rhoh20*g*PH*1.488*.000145;       %%psi
delpo=pf-po;                     %%psi
icQ=qo;                         %%gpm
icdelp=delpo;                   %%psi

function dydx=odes(jw,a1,k2)
dydx=zeros(2,1);

dydx(1)=-jw*a1;
dydx(2)= -k2*y(1)^1.67;

end 


function F=JW(lp,qo,delpio,k3,y)

F=lp*(y(2)-qo*delpio/y(1)*exp(z/(k3*y(1)^0.40))-z;
 
end 
xo=0;
X=@JW
jw=fsolve(JW,xo);

xspan=[0 50];
[x,y]=ode45(@odes,xspan,[icQ icdelp]);


Error in fsolve (line 242)
            fuser = feval(funfcn{3},x,varargin{:});

Error in mhlro (line 24)
jw=fsolve(@(z)JW(lp,qo,delpio,k3,y),xo);

Caused by:
    Failure in initial objective function evaluation.
    FSOLVE cannot continue.

FIrst is my function of differntial equations

followed by my function that i want to fsolve.

I want to find the number z in the equation but that equation is dependent on the differential equations and the differentials are depenedent on z.

The error i get is below.

[Walter Roberson]

@(z)JW(lp,qo,delpio,k3,y)

That ignores z, so fsolve would not be able to propose different input vectors as solutions.

Your code does not match the error message, which makes it confusing.

jw=fsolve(JW,xo);

That would try to invoke JW with no inputs, expecting that it would return a function handle that could be solved against.

[Rodrigo Blas]

Im sorry. Here it is updated..

clc, clear
a1=28*7*400;                        %%ft^2
po=40.6;                            %%psi
delpio=9;                           %%psi
qf=1525;                            %%gpm
qo=qf;
pp=16.4;                            %%psi
qp=1234;                            %%gpm
depr1=24.9;                         %%psi
delpr2=18.2;                        %%psi
PH=360;                                     %%ft
lp=2.76*.264/(60)^2*14.5;                   %%gal/m*min^2/psi
k2=1.75*10^-4*60^1.67*14.5/264.172^1.67;     %%psi/(gal/min)^1.67
k3=2.27*10^-2;                                  %%(m^3/h)^.6/m^2
g=32.17;                            %%ft/s^2
rhoh20=62.4;                        %%lbs/ft^3
pf=rhoh20*g*PH*1.488*.000145;       %%psi
delpo=pf-po;                     %%psi
icQ=qo;
icdelp=delpo;

xo=0;
x=@JW
jw=fsolve(JW,xo);

xspan=[0 50];
[x,y]=ode45(@odes,xspan,[icQ icdelp]);

 function dydx=odes(jw,a1,k2)
dydx=zeros(2,1);
dydx(1)=-jw*a1;
dydx(2)= -k2*y(1)^1.67;
 end 
 
 function F=JW(lp,qo,delpio,k3,y)

F=lp*(y(2)-qo*delpio/y(1)*exp(z/(k3*y(1)^0.40))-z;
 
 end 
 

 
x =

  function_handle with value:

    @JW

Error: File: JW.m Line: 3 Column: 50
Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for
mismatched delimiters.

Error in mhlro (line 24)
jw=fsolve(JW,xo);
 

[Walter Roberson]

F=lp*(y(2)-qo*delpio/y(1)*exp(z/(k3*y(1)^0.40))-z;
     1 2 1            2 1    2  3    4 3     21
     

Should be 0 by the end of the expression.

[Rodrigo Blas]

clc, clear
a1=28*7*400;                        %%ft^2
po=40.6;                            %%psi
delpio=9;                           %%psi
qf=1525;                            %%gpm
qo=qf;
pp=16.4;                            %%psi
qp=1234;                            %%gpm
depr1=24.9;                         %%psi
delpr2=18.2;                        %%psi
PH=360;                                     %%ft
lp=2.76*.264/(60)^2*14.5;                   %%gal/m*min^2/psi
k2=1.75*10^-4*60^1.67*14.5/264.172^1.67;     %%psi/(gal/min)^1.67
k3=2.27*10^-2;                                  %%(m^3/h)^.6/m^2
g=32.17;                            %%ft/s^2
rhoh20=62.4;                        %%lbs/ft^3
pf=rhoh20*g*PH*1.488*.000145;       %%psi
delpo=pf-po;                     %%psi
icQ=qo;
icdelp=delpo;

xo=0;
x=@JW
jw=fsolve(JW,xo);

xspan=[0 50];
[x,y]=ode45(@odes,xspan,[icQ icdelp]);

function dydx=odes(jw,a1,k2)
dydx=zeros(2,1);
dydx(1)=-jw*a1;
dydx(2)= -k2*y(1)^1.67;
end 

function F=JW(lp,qo,delpio,k3,y)

F=lp*(y(2)-qo*delpio/y(1)*exp(z/(k3*y(1)^0.40)))-z;
 
end 

>> JW

Not enough input arguments.

Error in JW (line 3)

F=lp*(y(2)-qo*delpio/y(1)*exp(z/(k3*y(1)^0.40)))-z;

This is the error I got.

[Walter Roberson]

As I wrote before:

jw=fsolve(JW,xo);

That would try to invoke JW with no inputs, expecting that it would return a function handle that could be solved against.

Remember that MATLAB evaluates all functions and expressions before passing them in to a function. With JW being a function, you are asking to invoke JW and to use whatever JW returns as the first parameter of fsolve() . The first parameter that reaches fsolve() must be a function handle: the first parameter in your call to fsolve() must be something that evaluates to a function handle. Including possibly an expression that builds a handle to an anonymous function.

[Rodrigo Blas]

xo=0;
x=@JW
jw=fsolve(x,xo);

Error in mhlro (line 24)
jw=fsolve(x,xo);

Caused by:
    Failure in initial objective function evaluation.
    FSOLVE cannot continue.
 

Is this what you mean by function handle?

[Walter Roberson]

Yes, that would be a function handle, and is closer to what you need. However your JW function is defined to take 5 inputs, but fsolve() is only going to pass one input to the function handle, so your JW function is not receiving enough inputs.

http://www.mathworks.com/help/matlab/math/parameterizing-functions.html

Reminder of what I posted earlier:

@(z)JW(lp,qo,delpio,k3,y)

That ignores z, so fsolve would not be able to propose different input vectors as solutions

[Rodrigo Blas]

function F=JW(lp,qo,delpio,k3,y,xo,z)

F=fsolve(@findjw,xo);


    function F=findjw(z)
F=lp*(y(2)-qo*delpio/y(1)*exp(z/(k3*y(1)^0.40)))-z;
 
    end 
end

Undefined function or variable 'y'.

Error in mhlro (line 23)
x=JW(lp,qo,delpio,k3,y,xo,z)
 

This is the function i created.

'Y' is the answer coming out of the other function after ode45 which im trying to use for this one (JW function).

Also, im sure itll say z is undefined, right?

Answer 1

[Walter Roberson]

function F=JW(lp,qo,delpio,k3,y,z)                          %<- z is an INPUT
  F=lp*(y(2)-qo*delpio/y(1)*exp(z/(k3*y(1)^0.40)))-z;
end