MATLAB: Hi all, I am trying to solve a fourth order differential equation using bvp4c.Below is the code.Can anyone help me to find the mistake in the code for which matlab is showing the following error?Thanks you

ode

function sol = Fig1

solinit=bvpinit(linspace(0,30,50),@guess);

sol=bvp4c(@cantileverode,@cantileverbc,solinit);

xint=linspace(0,30,50);

Sxint=deval(sol,xint);

axis('auto')

function dy=cantileverode(x,y,l,F)

         l=17.6e-3;
         F=0.026;
         dy=zeros(4,1);
         dy(1)=y(2);
         dy(2)=y(3);
         dy(3)=y(4);
         dy(4)=(1/l^2)*(y(3)+F*cos(y(1)));
function res=cantileverbc(ya,yb,l,F)
         res=[ya(1)
             ya(2)
             yb(3)
             yb(4)];

function v =guess(x)

v=[(30-x)^4*x^2*exp(x);-4*(30-x)^3*x^2*exp(x)+(30-x)^4*(x^2*exp(x)+2*x*exp(x))];

and the errors are as follows;

Attempted to access y(3); index out of bounds because numel(y)=2.

Error in Fig1>cantileverode (line 10) dy(2)=y(3);

Error in bvparguments (line 105) testODE = ode(x1,y1,odeExtras{:});

Error in bvp4c (line 129) [n,npar,nregions,atol,rtol,Nmax,xyVectorized,printstats] = …

Error in Fig1 (line 3) sol=bvp4c(@cantileverode,@cantileverbc,solinit);

Best Answer

You will have to supply guesses for y, y', y'' and y'''.

Your guess function only contains two components.

Best wishes

Torsten.

Related Solutions

MATLAB: Solve a system of second order coupled differential equations with bvp4c

In the definition of bvp_function, when MATLAB reaches the line

dYdx(2) = (Y(2) + Y(4)) * (num1 - Y(2) - dYdx(3)/Y(3) - dYdx(4));

at that time, the values of dYdx(3) and dYdx(4) are undefined, so MATLAB throws an error.

You can solve this problem, either by changing the order of calculation like this

function dYdx = bvp_function(x, Y)
% Y(1)=j, Y(2)=j', Y(3) = xsi, Y(4) = t 

    num1 = 2.331;
    dYdx(4) = -Y(2)*exp(Y(1));
    dYdx(3) = Y(2) + dYdx(4) - Y(3);
    dYdx(1) = Y(2);
    dYdx(2) = (Y(2) + Y(4)) * (num1 - Y(2) - dYdx(3)/Y(3) + dYdx(4));
    dYdx = dYdx(:);
end

or replace the values of c' and t' in equation 1 and 2 like this

function dYdx = bvp_function(x, Y)
% Y(1)=j, Y(2)=j', Y(3) = xsi, Y(4) = t 
    num1 = 2.331;
    dYdx(1) = Y(2);
    dYdx(2) = (Y(2) + Y(4)) * (num1 - Y(2) - (Y(2) - Y(2)*exp(Y(1)) - Y(3))/Y(3) + Y(2)*exp(Y(1)));             
    dYdx(3) = Y(2) - Y(2)*exp(Y(1)) - Y(3);
    dYdx(4) = -Y(2)*exp(Y(1));
    dYdx = dYdx(:);
end

However, even after this, there seems to be a singularity in your system of ODEs. You need to analyze your equations to see what might be causing the singularity.

MATLAB: I tried to solve fourth order differential equation using bvp4c.However, there seems to be an error while running it.Could you please let me know the potential mistake in the program?Thanks

You could test whether it works to save yb(1) to a global variable in "cantileverbc" and to access this variable in "cantileverode".