help to find error in this?

function Needle

a=0.01;

Pr=3.0;R=2.0;Nr=10;Ec=0.3;

solinit= bvpinit(linspace(a,40,100),[0 0 0 0 0]);

sol = bvp4c(@Needleode,@Needlebc,solinit);

eta = sol.x;

f = sol.y;

disp(f(2,1))

Cf=8*a^(1/2)*f(3);

disp(Cf)

function dfdeta = Needleode(eta,f)

f1_thetha=f(4)*(R-1)+1;

f2_thetha=eta*(1+4*(f1_thetha)^3/3*Nr);

dfdeta = [ f(2)

f(3)

-(1/(2*eta))*(f(1)*f(3)+2*f(3))

f(5)

-(f(5)+Pr*f(1)*f(5)/2+4*Ec*Pr*eta*(f(3))^2+2*f(5)*(f1_thetha)^3/3*Nr+4*eta*f(5)^2*(R-1)*(f1_thetha)^2/Nr)/f2_thetha

];

function res = Needlebc(f0,finf)

a=0.01;e=0.7;

res = [f0(1)-(a*e/2)

f0(2)-e/2

finf(2)-(1-e)/2

f0(1)-1

finf(1)-0

];

Error which i found is:

Undefined function or variable 'R'.

Error in Needle>Needleode (line 14)

f1_thetha=f(4)*(R-1)+1;

Error in bvparguments (line 105)

testODE = ode(x1,y1,odeExtras{:});

Error in bvp4c (line 130)

bvparguments(solver_name,ode,bc,solinit,options,varargin);

Error in Needle (line 5)

sol = bvp4c(@Needleode,@Needlebc,solinit);

>>

Answer 1

[Sulaymon Eshkabilov]

Here is the corrected code. But you need to check your Jacobian matrix formulations; otherwise, this exercise is not solvable:

global R Nr Pr Ec
a=0.01;
Pr=3.0;R=2.0;Nr=10;Ec=0.3;
solinit= bvpinit(linspace(a,40,100),[0 0 0 0 0]);
sol = bvp4c(@Needleode,@Needlebc,solinit);
eta = sol.x;
f = sol.y;
disp(f(2,1))
Cf=8*a^(1/2)*f(3);
disp(Cf)
function dfdeta = Needleode(eta,f)
global R Nr Pr Ec
 f1_thetha=f(4)*(R-1)+1;
f2_thetha=eta*(1+4*(f1_thetha)^3/3*Nr);
dfdeta = [ f(2);
           f(3);
        -(1/(2*eta))*(f(1)*f(3)+2*f(3));
        f(5);
        -(f(5)+Pr*f(1)*f(5)/2+4*Ec*Pr*eta*(f(3))^2+2*f(5)*(f1_thetha)^3/3*Nr+4*eta*f(5)^2*(R-1)*(f1_thetha)^2/Nr)/f2_thetha ];
end
function res = Needlebc(f0,finf)
a=0.01;e=0.7;
res = [f0(1)-(a*e/2);
       f0(2)-e/2;
       finf(2)-(1-e)/2;
       f0(1)-1;
       finf(1)-0];
end

[Walter Roberson]

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

global is not recommended

[Nk]

Error using bvp4c (line 251)

Unable to solve the collocation equations -- a singular Jacobian encountered.

Error in NK (line 6)

sol = bvp4c(@Needleode,@Needlebc,solinit);

it shows this error after running your code i couldn't understand how to fix it

[Sulaymon Eshkabilov]

Check the BC values and Jacobian matrix formualtions of your exercise.

Answer 2

[Torsten]

Your boundary conditions contradict each other:

f0(1)-(a*e/2)

f0(1)-1

So f(1) at x = 0.01 should be at the same time 0.01*0.7/2 = 0.0035 and 1. That's not possible.