Please help me. I want to run this attached simple code

%Error using ^

%Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and the power is a scalar. To perform elementwise matrix powers,

%use '.^'.

%Error in proj/projfun (line 42)

% dy(2) = (4*b1*m^2+4*m^2*(b2-lamda).*p+4*b3*m^2*(p).^2+4*b4*m^2*(p).^3+4*b5*m^2.*p^4+a*(2*m+1)*(dp).^2)/(-2*a*m(2*m+1)*p);

%

%code%
function sol= proj
clc;clf;clear;

myLegend1 = {};myLegend2 = {};
rr = [1 2 4]
for i =1:numel(rr)
    b1 = rr(i)
    b2=0.5;b3=0.5;b4=0.5;
    lamda=0.5;
y0 = [1,0,1,0,0,1,0,1];options =bvpset('stats','on','RelTol',1e-5);
    m = linspace(-20,20);
   solinit = bvpinit(m,y0);
      sol= bvp4c(@projfun,@projbc,solinit,options);
      
    figure(1)
    plot(sol.x,(sol.y(1,:))^0.5)
   % axis([0 4 0 1])
    grid on,hold on
    myLegend1{i}=['n= ',num2str(rr(i))];
    figure(2)
    plot(sol.x,(sol.y(2,:)))
        %axis([0 4 -0.8 0])

    grid on,hold on
    myLegend2{i}=['n = ',num2str(rr(i))];
    i=i+1;
end
figure(1)
legend(myLegend1)
hold on
figure(2)
legend(myLegend2)

    function dy= projfun(~,y)
        dy= zeros(8,1);
%         alignComments
         p = y(1);
        dp = y(2);
                 dy(1) = dp;        
          dy(2) = (4*b1*m^2+4*m^2*(b2-lamda).*p+4*b3*m^2*(p).^2+4*b4*m^2*(p).^3+4*b5*m^2.*p^4+a*(2*m+1)*(dp).^2)/(-2*a*m(2*m+1)*p);
    end
end
function res= projbc(ya,yb)

res= [ya(1);
    ya(2); 
    yb(1);
       yb(2);
      
   % yb(7);
    ];
end

Answer 1

[Torsten]

Use

function dy= projfun(x,y)

and replace m by x in the function.

Further, b5 and a are undefined.

Further, you miss a multiplication sign in this expression: (-2*a*m(2*m+1)*p) (in which you should already have replaced m by x).

Further, if you define a system of 2 differential equations, dy has to be of size 2, not 8. Thus you have to modify

y0 = [1,0,1,0,0,1,0,1]; and dy= zeros(8,1);

Same for the boundary conditions: you need 2, not 4.

[Tarek]

Thank you Mr Torsten

[Torsten]

You will get trouble with your dy(2) expression because you divide by (-2*a*m(2*m+1)*p) which is 0 for m = 0 and m = -1/2.

[Tarek]

Thanks alot Professor Torsten

Answer 2

[Matt J]

Do what the error message says. Use .^ instead of ^

[Tarek]

Hellow 👋 Mr Matt J.

Please help me.

The error is:

Error using ^

%Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and the power is a scalar. To perform elementwise matrix powers,

%use '.^'.

%Error in proj/projfun (line 42)

% dy(2) = (4*b1*m^2+4*m^2*(b2-lamda).*p+4*b3*m^2*(p).^2+4*b4*m^2*(p).^3+4*b5*m^2.*p^4+a*(2*m+1)*(dp).^2)/(-2*a*m(2*m+1)*p);

%

[Stephen23]

@Tarek:

What you used:

^

What Matt J and the error message advised you to use:

.^

https://www.mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html