Loop for bvp4c function with an unknown parameter

I tried to solve sixth order differential equation using bvp4c with an unknown parameter “S” and one variable parameter “k”. I have written a subroutine as a bvp4c and a main function for “k”.

The main code is written as follows:

function [] = main()

kk=0.5 ;

for i=1:60

    k=kk;

     valuePresentstudy = Surfactant(k); 

             kk=kk+0.1;

    end

 end

The bvp4c subroutine is written as follows:

function valuePresentstudy = Surfactant(k)

options = bvpset('NMax',100000);

S=0.28;

solinit = bvpinit(linspace(0,1,100),[0.1 0 0 0 0 0],S);

sol = bvp4c(@(x,y)fourode(x,y,k),@(ya,yb)fourbc(ya,yb,k),solinit,options);

save hatimsol.mat sol

x = linspace(0,1);

y = deval(sol,x);

valuePresentstudy=y;

%

function dydx = fourode(x,y,S,k)

Pr=10;

dydx = [ y(2); y(3); y(4); -(k^4+(S/Pr)*k^2)*y(1)+(2*(k^2)+(S/Pr))*y(3); y(6); (k^2+S)*y(5)-y(1)];

%

function res = fourbc(ya,yb,S,k)

e=0;

res = [ ya(1); ya(2); ya(5); yb(1); yb(6)+e*k*yb(5); yb(5)-1; yb(6)];

The error is given as:

Error using Surfactant>@(x,y)fourode(x,y,k)

Too many input arguments.

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 Surfactant (line 5)

sol = bvp4c(@(x,y)fourode(x,y,k),@(ya,yb)fourbc(ya,yb,k),solinit,options);

Error in MainPresentSurfactant (line 6)

     valuePresentstudy = Surfactant(k);

Could you please tell me where my mistake is?

Thanks in advance for your help.

Answer 1

[Torsten]

Maybe

sol = bvp4c(@(x,y,S)fourode(x,y,S,k),@(ya,yb,S)fourbc(ya,yb,S,k),solinit,options);

Otherwise pass k to fourode and fourbc as global.

Best wishes

Torsten.

[Ramin Rabani]

Thank you for your reply. it Worked for me. Thanks a lot for your help

Answer 2

[Torsten]

function [] = main()
kk=0.5 ;
for i=1:60
    k=kk;
     valuePresentstudy = Surfactant(k); 
             kk=kk+0.1;
    end
 end

function valuePresentstudy = Surfactant(k)
global kk

kk = k;
options = bvpset('NMax',100000);
S=0.28;
solinit = bvpinit(linspace(0,1,100),[0.1 0 0 0 0 0],S);
sol = bvp4c(@fourode,@fourbc,solinit,options);
save hatimsol.mat sol
x = linspace(0,1);
y = deval(sol,x);
valuePresentstudy=y;

%

function dydx = fourode(x,y,S)
global kk
Pr=10;
dydx = [ y(2); y(3); y(4); -(kk^4+(S/Pr)*kk^2)*y(1)+(2*(kk^2)+(S/Pr))*y(3); y(6); (kk^2+S)*y(5)-y(1)];

%

function res = fourbc(ya,yb,S)
global kk
e=0;
res = [ ya(1); ya(2); ya(5); yb(1); yb(6)+e*kk*yb(5); yb(5)-1; yb(6)];

Best wishes

Torsten.

[Tanya Sharma]

Hi Torsten, I am working on a similar kind of problem where S is unknown eigenvalue.

Can I evaluate eigenvalues S using bvp4c?

Answer 3

[Akmaral Pussurmanova]

I don't know where is a mistake( Can you help me?

function dxdt = mat4ode(t,x,mu) % equation being solved
alfa = 0;
dxdt = [x(2)
      -x(1)+0.1*(alfa*cos(2*t)*x(1)+x(1)^3)+mu*sin(2*t)+(1-pi^2)*sin(pi*t)+1-0.1*((sin(pi*t)+1)^3)-2*sin(2*t)];
end
%-------------------------------------------
function res = mat4bc(xa,xb,mu) % boundary conditions
res = [xa(1)-1
       xb(1)-1
       xa(2)-xb(2)];
end
%-------------------------------------------
function yinit = mat4init(t) % initial guess function
yinit = [sin(pi*t)+1
        pi*cos(pi*t)
         ];
end

mu=2;
  
solinit = bvpinit(linspace(0,2,20),@mat4init,mu);

sol = bvp4c(@mat4ode, @mat4bc, solinit);
fprintf('Fourth eigenvalue is approximately %7.3f.\n',...
            sol.parameters)

xint = linspace(0,2);
Sxint = deval(sol,xint);

plot(xint,Sxint)
axis([0 2 -4 4])
title('Eigenfunction of Mathieu''s Equation.') 
xlabel('x')
ylabel('y')
legend('y','y''')

[MINATI]

Dear

Akmaral

Post ur doubt in another question page and mail me the link @

[e-mail]