Solving third order nonlinear boundary value problem

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parham kianian
parham kianian 2020-12-21
编辑： Torsten 2023-10-1
I have a boundary value problem in this form:
where alpha is a nonzero constant and boudary conditions are:
f(-1) = 0
f(0) = 1
f(1) = 0
How can I solve this problem using bvp5c?
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PRITESH
PRITESH 2023-10-1
Hi @Torsten. Thanks for the reply. I am still confused while applying this technique. I am trying to use bvp4c and am getting singular Jacobian values.
Torsten
Torsten 2023-10-1
编辑：Torsten 2023-10-1
Ran in:
I am trying to use bvp4c and am getting singular Jacobian values.
I don't:
alpha = 1;
xc = 0;
xmesh = [linspace(-1,xc,1000),linspace(xc,1,1000)];
solinit = bvpinit(xmesh, [0 0 0]);
sol = bvp5c(@(x,y,r)f(x,y,r,alpha),@bc,solinit);
plot(sol.x,sol.y(1,:))
function dydx = f(x,y,region,alpha)
dydx = [y(2);y(3);-alpha*y(1)*y(2)-4*alpha^2*y(2)];
end
function res = bc(yl,yr)
res = [yl(1,1);yr(1,1)-1;yr(1,1)-yl(1,2);yr(2,1)-yl(2,2);yr(3,1)-yl(3,2);yr(1,2)];
end

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