Symbolic Integration of two functions that are the gradient of a function
2 views (last 30 days)
Show older comments
Neil Smith on 13 Feb 2020
Edited: Neil Smith on 24 Jan 2021
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.
Deepak Meena on 22 Jan 2021
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()
Find more on Symbolic Math Toolbox in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!Start Hunting!