I am getting the result and graphs of the equation yy1 but not YY2. if I remove the 2nd equation i.e yy2 part then the program is giving result. whenever m adding yy2 part and boundary conditions m getting error.can someone help me?

function [y]=wedge_bvp4c
% defining parameters
b=0.4,M=0.4,L=0.7,Pr=0.5,R= 0.5;
sol1   = bvpinit(linspace(0,5,10),[1 0 1 0 1 0]);
    sol    = bvp4c(@bvp2D,@bc2D,sol1);
    x      = sol.x;
    y      = sol.y; 
 
    %%% Plotting of the velocity
    figure (1)
    plot(x, y(2, :) ,'linewidth', 1)
    hold on
    xlabel('\eta', 'fontweight', 'bold', 'fontsize', 16)
    ylabel('f^/(\eta)', 'fontweight', 'bold', 'fontsize', 16)
    %% Residual of the boundary conditions
  function residual = bc2D(y0, yinf)         
     residual=[y0(1);  y0(2); y0(5)-1; yinf(2)-1; yinf(5)];      
  end

    %%  System of First Order ODEs
  function yvector = bvp2D(t,y)
        yy1 = (1/(1+1/b))*(M*y(2)-y(1)*y(3)-L*(1-y(2)*y(2)));
        yy2=  (1/(1+R))*Pr*(y(2)*y(5)-y(1)*y(6));
      yvector  = [y(2);y(3);y(5);y(6);yy1;yy2];
  end
end

Answer 1

[Torsten]

You always need as many boundary conditions as you have first-order differential equations. So if you have 6 equations, you need 6 boundary conditions, not 5.

Answer 2

[Star Strider]

There is an error somewhere.

According to the error, 'bc2D' '... should return a column vector of length 6.' It is returning a column vector of length 5 instead.

Please change whatever is necessary to let your code run.

wedge_bvp4c

Error using bvparguments (line 103)
Error in calling BVP4C(ODEFUN,BCFUN,SOLINIT):
The boundary condition function BCFUN should return a column vector of length 6.

Error in bvp4c (line 119)
bvparguments(solver_name,ode,bc,solinit,options,varargin);
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Error in solution>wedge_bvp4c (line 11)
sol = bvp4c(@bvp2D,@bc2D,sol1);
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

function [y]=wedge_bvp4c
% defining parameters
b=0.4;
M=0.4;
L=0.7;
Pr=0.5;
R= 0.5;
sol1   = bvpinit(linspace(0,5,10),[1 0 1 0 1 0]);
    sol    = bvp4c(@bvp2D,@bc2D,sol1);
    x      = sol.x;
    y      = sol.y; 
 
    %%% Plotting of the velocity
    figure (1)
    plot(x, y(2, :) ,'linewidth', 1)
    hold on
    xlabel('\eta', 'fontweight', 'bold', 'fontsize', 16)
    ylabel('f^/(\eta)', 'fontweight', 'bold', 'fontsize', 16)
    %% Residual of the boundary conditions
  function residual = bc2D(y0, yinf)         
     residual=[y0(1);  y0(2); y0(5)-1; yinf(2)-1; yinf(5)];      
  end

    %%  System of First Order ODEs
  function yvector = bvp2D(t,y)
        yy1 = (1/(1+1/b))*(M*y(2)-y(1)*y(3)-L*(1-y(2)*y(2)));
        yy2=  (1/(1+R))*Pr*(y(2)*y(5)-y(1)*y(6));
      yvector  = [y(2);y(3);y(5);y(6);yy1;yy2];
  end
end

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