I am pretty new to MATLAB. I am try to use ode 45 to solve a differential equation arising from a multiple source boundary condition. I want to use a for loop for the boundary condition, but I guess I am missing something

function Temp = proj(x,h)

b=h(1);

g=h(2);

v=20;

a=0.5;

k=45;

q=5000;

Temp(1,1)=g;

for x=0:200

    if x<20 

        Temp(2,1)=(e^((v*x)/(2*a))*(q/k))- ((v*b)/(2*a));

    else
        Temp(2,1) = 0;

    end
end

h0=[0;0];

xSpan=[0,200];

[xSol,hSol]=ode45(@(x,h) proj(x,h), xSpan, h0);

plot(xsol,hSol(:,1)+22);

Answer 1

[Stephan]

Hi,

maybe it is better to integrate this function stepwise, since your function is not smooth, because of the if-else statement - try:

h1=[0;0];
xSpan1=[0,20];
[xSol1,hSol1]=ode45(@(x,h) proj(x,h), xSpan1, h1);

h2=[hSol1(end,1), hSol1(end,2)];
xSpan2=[20,200];
[xSol2,hSol2]=ode45(@(x,h) proj(x,h), xSpan2, h2);

semilogy(xSol1,hSol1(:,1)+22,'r--',xSol2,hSol2(:,1)+22,'r-');

function Temp = proj(x,h)
b=h(1);
g=h(2);
v=20;
a=0.5;
k=45;
q=5000;
Temp(1,1)=g;

if x<20
    Temp(2,1)=(exp((v*x)/(2*a))*(q/k))- ((v*b)/(2*a));
else
    Temp(2,1) = 0;
end
end

gives:

Best regards

Stephan

[David Akinpelu]

Thanks.

[David Akinpelu]

Hello, I think I am having a semantic error. the idea is to solve the ode Y" = (v*q*x)/k for all values of x between 0 and 20 and Y" = 0, for all values of x between 20 and 200. I keep getting the a constant value for all values of x in the plot. below is the code:

function Temp = proj(x,h)

b=h(1);

g=h(2);

v=20;

a=0.5;

k=45;

q=5000;

Temp(1,1)=g;

for x=0:20

    Temp(2,1)= (v*q*x)/k;

end

for x=21:200

    Temp(2,1) = 0;

end

end

h1=[0;0];

xSpan1=[0,20];

[xSol1,hSol1]=ode45(@(x,h) proj(x,h), xSpan1, h1);

h2=[0,0];

xSpan2=[20,200];

[xSol2,hSol2]=ode45(@(x,h) proj(x,h), xSpan2, h2);

plot(xSol1,hSol1(:,1)+22,'b--',xSol2,hSol2(:,1)+22,'r-');