Symbolic Integration of two functions that are the gradient of a function

Question

Neil Smith 2020-2-13

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/505401-symbolic-integration-of-two-functions-that-are-the-gradient-of-a-function

编辑： Neil Smith 2021-1-24

Is it possible to get matlab to do a symbolic integration of a gradient where you know that each term is dependent only on one variable?

I'm trying to get Matlab to do the following:

syms P(r,z) rho g omega P_atm
ode1 = diff(P,z) == rho * g
ode2 = diff(P,r) == rho * omega^2 / r
ode_total = ode1 + ode2
cond = P(0,0) = P_atm
soln(r,z) = dsolve(ode_total, cond);

Essentially, I'm trying to do the following:

Given the following pressure gradient in two dimensions (or three, where

), solve for the pressure as a function of r and z [and θ]:

,

using the relation:

and boundary condition:

How do I code the above process to result in the following solution (or is it even possible)?

As you might have guessed, these equations are derived from navier-stokes.

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

Deepak Meena 2021-1-22

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/505401-symbolic-integration-of-two-functions-that-are-the-gradient-of-a-function#answer_603593

在 MATLAB Online 中打开

Hi Neil,

I think on the line no 7 you meant :

cond = P(0,0) == P_atm

Now coming to your question dsolve is used to solve differential equation with one independent variable.

To Solve partial differntial equation I advised you to use pdepe()

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Neil Smith 2021-1-24

编辑：Neil Smith 2021-1-24

I think I ended up taking a different approach to get it working. I finished that course 9 months ago, so I don't remember, now...

Thanks for your response, anyway

请先登录，再进行评论。

Symbolic Integration of two functions that are the gradient of a function

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

回答（1 个）

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

另请参阅

类别

标签

产品

Community Treasure Hunt

Symbolic Integration of two functions that are the gradient of a function

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

回答（1 个）

1 个评论 显示 -1更早的评论隐藏 -1更早的评论

另请参阅

类别

标签

产品

Community Treasure Hunt

WeChat

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

1 个评论
显示 -1更早的评论隐藏 -1更早的评论