BVP4C for solving an 3rd order ODE

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I am stuck in boundary condition which can't be slove with ode45.
to solve this problem can you please help me with boundary condition and convert it BVP4C ?
my progress is -
tRange = [0 10];
function dYdt = odefun(t,Y)
% Extract Y1,Y2,Y3 the element of Y
Y1 = Y(1);
Y2 = Y(2);
Y3 = Y(3);
% Expression for dY1dt, dY2dt,dY3dt.
dY1dt = Y2;
dY2dt = Y3;
dY3dt = -(1/2)*Y1*Y3;
% Create dYdt, column vector containing dY1dt, dY2dt, and dY3dt
dYdt = [dY1dt; dY2dt; dY3dt];
end

Accepted Answer

Torsten
Torsten on 29 Sep 2022
tmesh = linspace(0,10,100);
solinit = bvpinit(tmesh, [0 1 0]);
sol = bvp4c(@odefun, @bcfcn, solinit);
plot(sol.x, sol.y)
function dYdt = odefun(t,Y)
% Extract Y1,Y2,Y3 the element of Y
Y1 = Y(1);
Y2 = Y(2);
Y3 = Y(3);
% Expression for dY1dt, dY2dt,dY3dt.
dY1dt = Y2;
dY2dt = Y3;
dY3dt = -(1/2)*Y1*Y3;
% Create dYdt, column vector containing dY1dt, dY2dt, and dY3dt
dYdt = [dY1dt; dY2dt; dY3dt];
end
function res = bcfcn(ya,yb)
res = [ya(1);ya(2);yb(2)-1];
end
  2 Comments
Torsten
Torsten on 29 Sep 2022
Yes, and sol.y(3,:) is d^2y/dt^2.

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