I want to solve a multi point boundary condition differential equation. I keep getting error on my Bvp4c line, I tried debugging it, but could resolve the error.

function rhs = bvp_rhs(x,T)

rhs=[T(2); ((v/(2*a))^2)* T(1)];

function bc=bvp_bc(Tl,Tm,Tr)

bc=[Tl(1);Tm(21);(1/k)*e^(vx/(2*a))*(Tr(2)(200)+(Tr(1)(200)(v/(2*a))))];

x = linspace(1,200);

a = 0.25;

v=20;

k=45;

q=0.005;

solinit=bvpinit(linspace(1,200),[0,0]);

sol = bvp4c(@bvp_rhs,@bvp_bc,solinit);

BS=deval(sol,x);

plot(x,BS);

Answer 1

[Stephan]

Hi,

there are several Problems in your code:

bc=[Tl(1);Tm(21);(1/k)*exp(vx/(2*a))*(Tr(2)(200)+(Tr(1)(200)(v/(2*a))))];

produces error because:

Tr(2)(200)+(Tr(1)(200)(v/(2*a)))

is not a valid Matlab syntax, maybe you mean:

Tr(2) * 200 + (Tr(1) * 200 * (v/(2*a)))   or
Tr(2) + 200 + (Tr(1) + 200 + (v/(2*a)))

however, this has to be fixed.

--------------

Next Problem - If you want to express

e^x

in Matlab, the syntax is:

exp(x)

So if you fix this a valid line of Matlab code could look like this:

bc=[Tl(1);Tm(21);(1/k)*exp(vx/(2*a))*(Tr(2)*(200)+(Tr(1)*(200)*(v/(2*a))))];

But this has to be checked by you, because i made just a guess / an example.

------------

Next problem - When you fixed your equation to something valid, the variables v,a, and k are unknown in the functions. Fix this with a nested structure like this:

function solve_bvp
x = linspace(1,200);
a = 0.25;
v=20;
k=45;
q=0.005;
solinit=bvpinit(linspace(1,200),[0,0]);
sol = bvp4c(@bvp_rhs,@bvp_bc,solinit);
BS=deval(sol,x);
plot(x,BS);

function rhs = bvp_rhs(x,T)
rhs=[T(2); ((v/(2*a))^2)* T(1)];
end

function bc=bvp_bc(Tl,Tm,Tr)
bc=[Tl(1);Tm(21);(1/k)*exp(vx/(2*a))*(Tr(2)*(200)+(Tr(1)*(200)*(v/(2*a))))];
end
end

---------------

Next problem - Index exceeds array bounds:

Sure that

Tm(21)

can be correct? It should be Tm(1) or Tm(2) i guess.

----------------

Next problem - Undefined function or variable 'vx'. I guess

exp(vx/(2*a))

should be

exp(v*x/(2*a))

then this error is fixed - Or is there a missing variable vx?

-----------------

There are more errors in this code - i stopped debugging, because i think you should fix this so far, read about Matlab fundamentals and come back if you have done so far.

Best regards

Stephan