4th order ODE, 4 boundary conditions

Question

Connor Thompson 2022-7-11

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1757380-4th-order-ode-4-boundary-conditions

回答： MOSLI KARIM 2023-2-16

I have a 4th order ODE, with 4 boundary conditions.

The ODE problem is

y''''(x) = y(x)*y'''(x) - y'(x)*y''(x)

With the 4 boundary conditions:

y(0) = 0.1, y(1) = 0, y'(0) = 0, y'(1) = 0.

I started off my code by writing the ODE as a system of first order ODE's,

function dydx = ab(x,y)

dydx = zeros(4,1);

dydx(1) = y(2);

dydx(2) = y(3);

dydx(3) = y(4);

dydx(4) = y(1)*y(4) - y(2)*y(3);

Then defining the 4 boundary conditions,

function res = bc4(ya,yb)

res = [ya(1)-0.1; yb(1); ya(2); yb(2)];

Followed by:

solinit = bvpinit(linspace(0,0.05,1), [1, 0]);

sol = bvp4c(@ab, @bc4,solinit);

x = linspace(0,1);

y = deval(sol.x);

plot(x,y(1,:));

However, I already get an error on the second line,

"Not enough input arguements. Erron in __ (line 3)

dydx = y(2)"

Any ideas on what is going wrong?

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Answer 1

Torsten 2022-7-11

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1757380-4th-order-ode-4-boundary-conditions#answer_1004665

编辑：Torsten 2022-7-11

在 MATLAB Online 中打开

%solinit = bvpinit(linspace(0,0.05,1), [1, 0]);

solinit = bvpinit(0:0.05:1, [1, 0,0,0]);