How can I solve this BVP problem which is second-order ODE with variable coefficient?
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Sohrab Askarli
on 29 Nov 2020
Commented: Sohrab Askarli
on 30 Nov 2020
Hi there,
I have some problems regarding solving this problem on MATLAB:
y'' + [(1-10x^2)/x]*y' = 0
BC: y(0) = 1, y(1) = 0
Thanks in advance.
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Accepted Answer
Stephan
on 30 Nov 2020
Edited: Stephan
on 30 Nov 2020
Your function handle appears to be incorrect:
syms y(x)
eq = diff(y,x,2) + ((1-10*x^2)/x)*diff(y,x,1) == 0;
[V,S] = odeToVectorField(eq);
fun = matlabFunction(V,'Vars',{'x','Y'})
gives:
fun =
function_handle with value:
@(x,Y)[Y(2);((x.^2.*1.0e+1-1.0).*Y(2))./x]
additionally your function gets singular at x=0, to avoid this:
fun = @(x,Y)[Y(2);((x.^2.*1.0e+1-1.0).*Y(2))./x];
bc = @(ya, yb) [ya(1) - 1; yb(1)];
xmesh = linspace(1e-4, 1, 100);
solinit = bvpinit(xmesh, [1 0]);
sol = bvp4c(fun, bc, solinit);
figure;
yyaxis left
plot(sol.x, sol.y(1,:),'LineWidth',2)
yyaxis right
semilogy(sol.x, sol.y(2,:),'LineWidth',2)
Note that the right axis is log scaled:
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