BVP4C for solving an 3rd order ODE

Question

Syed Arafun Nabi 2022-9-29

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1814245-bvp4c-for-solving-an-3rd-order-ode

编辑： Torsten 2023-12-2

采纳的回答： Torsten

在 MATLAB Online 中打开

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

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Answer 1

Torsten 2022-9-29

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1814245-bvp4c-for-solving-an-3rd-order-ode#answer_1063100

在 MATLAB Online 中打开

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

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Shriram 2023-12-1

Thanks for your answer!

I was curious about how to implemenet this method for a problem where the boundary conditions are as follows:

y(0) = 0, y'(2) = 0 and y'(10) = 1?

How would we formulate this in MATLAB?

Torsten 2023-12-2

编辑：Torsten 2023-12-2

You need two conditions at t = 2, not only one. Then you can solve the problem first from t=0 to t=2 with a total of 3 boundary conditions (one at t=0, two at t=2) and continue solving from t=2 to t=10, again with a total of three conditions given (two at t=2, one at t=10).

Note that the solution might have some discontinuous derivatives in t=2.

If you only prescribe a total of three conditions, there is no unique solution to the problem. BVP4C cannot be used in this case. Sometimes it's possible to get a parameter-dependent solution with "dsolve".

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