Third Order Boundary Value Problem (BVP) with Boundary Coditions only in Terms of Derivatives

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Saeid
Saeid 2020-7-7
评论： Saeid 2020-7-8
I need to solve the boundary value problem (related to flow of fluids in conical ducts):
Y''' + 1 - Y'^2 = 0
with all the three BCs bing only on the derivatives of Y (and none on Y itself):
Y'(0)=Y"(inf)=0
Y'(inf)=1
By formulating the problem exactly as suggested here:
https://de.mathworks.com/matlabcentral/answers/52075-solving-a-third-order-non-linear-ode-using-ode45
dYdX = @(X,Y) [Y(2); Y(3); Y(2).^2-1]; % Differential equation
res = @(ya,yb) [ya(2); yb(3); yb(2)-1];
SolYinit = bvpinit([0 5], [0; 0; 0]);
Fsol = bvp4c(dYdX, res, SolYinit);
X = Fsol.x;
Y = Fsol.y;
I tried to solve the problem, but received the Jacobian error.
Is it possible that the error is generated because the BCs do not contain Y(...), and is there a way around his problem?
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darova
darova 2020-7-8
I mean this
Y'(0)=Y"(inf)=0
Y'(inf)=1
res = @(ya,yb) [ya(2); yb(3); yb(2)-1];
THere are only derivatives. There should be at least one Y(0) or Y(inf) (starting or final position)
Saeid
Saeid 2020-7-8
That's what I suspected, thanks! Then I guess the way the problem is posed in the original literature source is not right.

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