Boundary condition Problem solving using bvp4c

I was given this ODE problem:

g" + (1/2a) g' n = 0, where n = x/t^1/2, g(n) = T (x,t) BC1: g(0) = Ts = 100; BC2: g(infinity) = Ti = 10; Find g(n) and plot

I created 2 m.file

 1) 
function [ eqn ] = eqn1( n,g )

%Material Iron

rho = 7897;

Cp = 452;

k = 73;

alpha = k/(rho*Cp);

eqn =[g(2);(-n*g(2))/(2*alpha)];

end

2) function [ BCs ] = BC(g_0,g_inf)

Ts = 100;

Ti = 10;

BCs =[g_0(1)-Ts,g_inf(1)-Ti];

end

Then solution I tried to use bvp4c to solve for the equation

sol=bvpinit(linspace(0,1,25),[0 1]);

sol=bvp4c(@eqn1,@BC,sol)

I got this : Undefined function 'eqn1' for input arguments of type 'double'.

Error in bvparguments (line 106) testODE = ode(x1,y1,odeExtras{:});

Error in bvp4c (line 130) [n,npar,nregions,atol,rtol,Nmax,xyVectorized,printstats] = ...

Please Point out where did i do wrong and how can i fix it. THanks in advance.

Answer 1

[Torsten]

You arranged your code as

function main

solinit=bvpinit(linspace(0,1,25),[0 1]);

sol=bvp4c(@eqn1,@BC,solinit)

function [ eqn ] = eqn1( n,g )

%Material Iron

rho = 7897;

Cp = 452;

k = 73;

alpha = k/(rho*Cp);

eqn =[g(2);(-n*g(2))/(2*alpha)];

function [ BCs ] = BC(g_0,g_inf)

Ts = 100;

Ti = 10;

BCs =[g_0(1)-Ts ; g_inf(1)-Ti];

?

Best wishes

Torsten.

Answer 2

[Khoa Ngo]

For the same problem, now I solve using dsolve('D2g+t*Dg/(2*a)=0') and it gave me some crazy equation: g(t)=((2^(3/4)*exp(t^2/(4*a))*(t^2/a)^(1/4)*(C44 + C45*pi^(1/2) - C45*pi^(1/2)*erf(((2^(1/2)*(t^2/a)^(1/2) ))/2))))/(2*t^(1/2)*exp(t^2/(2*a))^(1/2) )

Basically, I cant input the boundary condition g(0) and g(inf) to solver for C44 and C45.

Please help.

[Torsten]

I get as solution

g(x)=Ts+(Ti-Ts)*erf(x/(2*sqrt(a))).

where erf is the error function.

Best wishes

Torsten.