4th order ODE, boundary conditions problem

I am trying to solve a 4th order linear ODE with boundary conditions. I'm just learning to use bvp4c. The code is the following:

function mat4bvp
solinit = bvpinit(linspace(0,1,5),[1 0 0 0]);
sol = bvp4c(@mat4ode,@mat4bc,solinit);
x = linspace(0,1);
y = deval(sol,x);
plot(x,y(1,:));

function dxdy = mat4ode(x,y);
eps=0.1;
dp=[y(2)  
    y(3)    
    y(4)    
    2.*pi^2.*y(3) +(1./eps).*y(2)-pi^4.*y(1)];

function res = mat4bc(ya,yb);
res=[ya(1)     
     yb(1)     
     yb(3)     
     yb(4)];

But I get the following error message:

??? Error using ==> vertcat?CAT 
arguments dimensions are not consistent.
Error in ==> 4odecode>mat4ode at 13 
dp=[y(2)

?? Error in ==> bvparguments at 122    
testODE = ode(x1,y1,odeExtras{:});

Error in ==> bvp4c at 120
[n,npar,nregions,atol,rtol,Nmax,xyVectorized,printstats] =
...

Error in ==> 4odecode at 4?
sol = bvp4c(@mat4ode,@mat4bc,solinit);

Answer 1

[Andrew Newell]

In the assignment to dp (which, by the way, should be dxdy), the fourth line has a space in it which MATLAB thinks is separating two elements. With a couple more corrections, the code is

function mat4bvp

solinit = bvpinit(linspace(0,1,5),[1 0 0 0]);

sol = bvp4c(@mat4ode,@mat4bc,solinit);

x = linspace(0,1);

y = deval(sol,x);

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

function dxdy = mat4ode(~,y)

eps=0.1;

dxdy=[y(2)
      y(3)
      y(4)
      2.*pi^2.*y(3)+(1./eps).*y(2)-pi^4.*y(1)];

function res = mat4bc(ya,yb)

res=[ya(1)
  yb(1)
  yb(3)
  yb(4)];

Answer 2

[Gualtiero]

The solution seem to be extremely sensitive to the form that I give to solinit. Is there any general method to impose a suitable solinit?

Answer 3

[Gualtiero]

in particular, my 4th order ode is

y'''' -2*(pi^2)*y''-(1/eps)*y'+(pi^4)*y=0

b.c.: y(0)=y(1)=0; y''(1)=0; y'''(1)=0

it is not trivial to me to pose an initial guess that would give me the right answer...

[Andrew Newell]

What do you mean by the right answer?

Answer 4

[Gualtiero]

edit: an initial guess that satisfy the b.c. is

y=sin(x*pi)*cos(x*pi)+2*(pi^3)*(-(1./3)*(x^3)+(x^2)+(2./3)*x)

However, changing the number of meshpoints in linspace changes drastically the shape of the solution...

[MINATI]

@ Gualtiero

How do you know the initial guess as mentioned