- #1
bugatti79
- 794
- 1
Folks,
I am looking at the Ritz method for the following problem
##\displaystyle -\frac{d^2 u}{dx^2}-u+x^2=0## for ##0<x<1##
with boundary conditions ##u(0)=0## and ##\displaystyle \frac{du}{dx} |_{x=1} =1##
The last derivative term, how do I know whether that is a natural or essential BC?
I have googled the following guidelines but I am still confused.
Specification of the primary variable ( u in this case) is an essential BC*
Specification of a secondary variable (like a force F, not present in this example) is a natural boundary condition
IF a boundary condition involves one or more variables in a 'direct' way it is essential otherwise it is natural.
Direct implies excluding derivative of the primary function.**
I find this info conflicting based on * and **
I think the book states it is a natural BC.
Would appreciate some clarification...
THanks
I am looking at the Ritz method for the following problem
##\displaystyle -\frac{d^2 u}{dx^2}-u+x^2=0## for ##0<x<1##
with boundary conditions ##u(0)=0## and ##\displaystyle \frac{du}{dx} |_{x=1} =1##
The last derivative term, how do I know whether that is a natural or essential BC?
I have googled the following guidelines but I am still confused.
Specification of the primary variable ( u in this case) is an essential BC*
Specification of a secondary variable (like a force F, not present in this example) is a natural boundary condition
IF a boundary condition involves one or more variables in a 'direct' way it is essential otherwise it is natural.
Direct implies excluding derivative of the primary function.**
I find this info conflicting based on * and **
I think the book states it is a natural BC.
Would appreciate some clarification...
THanks