Integrating a 2nd order ODE

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PetronasAMG
PetronasAMG on 16 Oct 2021
Answered: Star Strider on 17 Oct 2021
I am given an equation,
d^2y/dx^2 + q(x) = 0
x ranges from 0 to 1 and y(0) = 1 and y(L) = 1.5
where L = 1
and q(x) = 2*cos((pi*x)/L)
here is what I have
function dydx = yfunc (x,y)
x = linspace(0,1,30);
L = 1;
for i = 1:length(x)
qx(i)= 2*cos((pi*x(i))/L);
end
dydx= -qx;
end
%main script
[x,y] = ode45(@yfunc,x,[1 1.5]);
I am running into an error stating Dimensions of arrays being concatenated are not consistent. Could you please help me?

Accepted Answer

Star Strider
Star Strider on 17 Oct 2021
This is a boundary value problem. Use bvp4c to solve it.
syms y(x) x L Y
q(x) = 2*cos(pi*x/L);
Dy = diff(y);
D2y = diff(Dy);
ODE = D2y + q
ODE(x) = 
[VF,Subs] = odeToVectorField(ODE)
VF = 
Subs = 
bvpfcn = matlabFunction(VF, 'Vars',{x,Y,L})
bvpfcn = function_handle with value:
@(x,Y,L)[Y(2);cos((x.*pi)./L).*-2.0]
I solved it completely, however I do not want to deprive you of the same feeling of accomplishment, so I leave the rest to you. It is a straightforward solution. Follow the examples in the documentation I linked to.
.

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