Coupeling of three equations BVP

Question

Thanh Hoang 2024-6-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2129256-coupeling-of-three-equations-bvp

评论： Torsten 2024-6-17

Dear all,

I have a maths understanding problem with the following code. I tried to couple three ode equations with another and solved them with a bvp solver. As for the boundary conditions I applied all (just as an example) to the second derivative since in my problem I want to set Newmann boundary conditions.

However, what I noticed is that I am not able to give the third equation a dependence on C. The system is only solvable with Eq. dydx(6) decoupled from C.

How would I be able to solve the system with including a dependence of Eq. dydx(6) with C. Is a boundary condition to dydx(1), dydx(3) or dydx(5) nessecary in all cases if I want to solve this kind of system? I hope somebody more gifted in maths can help me with that.

Thanks for you help!

clear all;

close all;

clc;

xmesh = linspace(0, 1, 100);

sol_init = bvpinit(xmesh, [0 0 1 0 0 1]);

sol = bvp4c(@ode, @bcfun, sol_init);

plot(sol.x, sol.y)

function dydx = ode(x,y)

A = y(1);

B = y(3);

C = y(5);

S = exp(A*B)-C;

dydx(1) = y(2);

dydx(2) = S;

dydx(3) = y(4);

dydx(4) = -S;

dydx(5) = y(6);

dydx(6) = exp(A+B);

% dydx(6) = C;

end

function res = bcfun(ya, yb);

res(1) = ya(2);

res(2) = yb(2);

res(3) = ya(4);

res(4) = yb(4);

res(5) = ya(6);

res(6) = yb(6);

end

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

James Blanchard 2024-6-17

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2129256-coupeling-of-three-equations-bvp#answer_1472881

I get errors with both choices for dydx(6). They seem to result from your initial guesses (sol_init). Try something different.

2 个评论
显示无隐藏无

Thanh Hoang 2024-6-17

在 MATLAB Online 中打开

Hey sorry, yes you are right! I had a different expresion for dydx(6) originally:

dydx(6) = exp(A+B)

Here the corrected code

clear all;

close all;

clc;

xmesh = linspace(0, 1, 100);

sol_init = bvpinit(xmesh, [0 0 1 0 0 1]);

sol = bvp4c(@ode, @bcfun, sol_init);

Warning: Unable to meet the tolerance without using more than 1666 mesh points.
The last mesh of 892 points and the solution are available in the output argument.
The maximum residual is 0.0520983, while requested accuracy is 0.001.

plot(sol.x, sol.y)

function dydx = ode(x,y)

A = y(1);

B = y(3);

C = y(5);

S = exp(A*B)-C;

dydx(1) = y(2);

dydx(2) = S;

dydx(3) = y(4);

dydx(4) = -S;

dydx(5) = y(6);

dydx(6) = exp(A+B);

% dydx(6) = C;

end

function res = bcfun(ya, yb);

res(1) = ya(2);

res(2) = yb(2);

res(3) = ya(4);

res(4) = yb(4);

res(5) = ya(6);

res(6) = yb(6);

end

Torsten 2024-6-17

在 MATLAB Online 中打开

There is no solution from bvp4c for

dydx(6) = exp(A+B);

either (see above).

The reason is that your equations only fix the derivative of y(5). So in my opinion, y(5) is only fixed by your equations up to an additive constant.

请先登录，再进行评论。

Coupeling of three equations BVP

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

回答（1 个）

2 个评论
显示无隐藏无

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

Coupeling of three equations BVP

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

回答（1 个）

2 个评论 显示 无隐藏 无

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

2 个评论
显示无隐藏无