How to use bvp4c for boundary value problem with 2 unknown parameters?

I have written the following code to solve the following coupled equations using bvp4c.

f′′− (a^2)*f = a*RaT*g

g′′− (a^2)*g = a*f

with x=0,1 f=0 g=0

where 'a' and 'Rat' are unknown parameters

errors

Reference to non-existent field 'r'.

Error in bvp_4 (line 7)

fprintf('For r=%f a= %f \n',sol.r(1),sol.r(2));

%-------------

clear all;

r=[5 1]; %initial guess value for unknowns

options=[];%dummy parameter

x=linspace(0,1,50);

solinit=bvpinit(linspace(0,1,10),ones(4,1),r);

sol=bvp4c(@frhs,@bvpbc,solinit,options);

fprintf('For r=%4.2f a= %4.2f \n',sol.r(1),sol.r(2));

bs=deval(sol,x);

hold on

plot(x,bs(1,:));

plot(x,bs(3,:),'*');

for i=1:4

    sol=bvp4c(@frhs,@bvpbc,sol,options);

    fprintf('For r=%4.2f || a= %4.2f \n',sol.r(1),sol.r(2));
    bs=deval(sol,x);

    plot(x,bs(1,:));
    plot(x,bs(3,:),'*');

end

%converting to first order equations

function rhs=frhs(x,y,r)

rhs=[y(2)

     r(2)*r(2)*y(1)+r(2)*r(1)*y(3)

     y(4)

     r(2)*r(2)*y(3)+r(2)*y(1) ];

end

%boundary conditions

function bc=bvpbc(yl,yr,r)

bc=[yl(1)

    yl(3)

    yl(2)-1 

    yr(1)

    yr(3)

    yr(4)-1];

end

%additional conditions applied 'yr(4)-1' and 'yl(2)-1 ' for two parameters

Answer 1

[Torsten]

fprintf('For r=%4.2f a= %4.2f \n',sol.parameters);

Best wishes

Torsten.

Answer 2

[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''')