MATLAB Coding for BVP

function res = mat4bc(ya,yb)

res = [ ya(1)-1

yb(2)

ya(3)

yb(4) ];

The above is for 2 boundary conditions. I need the coding for 3 conditions.

function sol=ex4

ex4init=bvpinit(linspace(0,100),[0 1 0 -1]);

sol=bvp4c(@ex4ode, @ex4bc, ex4init)

end

function f=ex4ode(x,y)

f=[y(2)

-x*x*y(2)

y(4)

-x*x*y(4)

];

end

function res=ex4bc(ya,yb,yc)

res=[ya(1)-3.462*10^(-22)

ya(3)-2.017

yb(1)-1

yb(3)

yc(2)+yc(4)

];

end

This is my program. when I run this program, I'm getting an error. Can someone tell me what is the error here?

[Torsten]

You can define boundary conditions for the solution variables at x=a (using ya) and at x=b (using yb). So I don't understand what yc is meant to represent in your code.

Maybe you could include the mathematical description of your problem.

[Joy Salomi]

These are my boundary conditions.

At x=infinity, u=1, v=0

At x=0, u=3.462*10^-22 and v=2.017

At x=lambda, du/dx = - dv/dx

what is the matlab code for this?

[Torsten]

Your solutions for u and v are already determined by the four conditions at x=0 and x=infinity. You can't impose a fifth boundary condition.

[Joy Salomi]

Okay sir. Thank you so much for your response. I'll try.

[Torsten]

Maybe of interest for you:

https://www.wolframalpha.com/input/?i=y''(t)%2Bt%5E2*y'(t)%3D0

This code gives you the solution for your system:

function main
  fun = @(t,c1,c2)c1*gamma(1/3)*gammainc(t.^3/3,1/3,'upper')/3^(2/3)+c2;
  c2u = 1;
  c1u = (3.462e-22-1)*3^(2/3)/gamma(1/3);
  c2v = 0;
  c1v = 2.017*3^(2/3)/gamma(1/3);
  t = linspace(0,20,200);
  u = fun(t,c1u,c2u);
  v = fun(t,c1v,c2v)
  plot(t,u,t,v)
end

Maybe your question was to determine lambda where du/dx = -dv/dx ?

[Joy Salomi]

Thank you for your reply Sir.