- #1
sunon77
- 2
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For a general dynamic system: dXi/dt = Fi(X1, X2,...,Xn), i=1,...,n,
Q.1
do you have some ideas of the existence conditions of following PDE:
a) (grad U, grad U + F) = 0 in n-dimension domain, (,) is inner product;
b) U >=0
Does it need a first type or second type of boundary condition?
Q.2
If solution does exist, how to solve it numerically?
- I tried to write in differential equation in matrix format, then apply Newton method. It is very difficult to have a converge scheme.
A more detailed simple example is attached to explain the solution that I tried.
Many thanks for your ideas or comments
Q.1
do you have some ideas of the existence conditions of following PDE:
a) (grad U, grad U + F) = 0 in n-dimension domain, (,) is inner product;
b) U >=0
Does it need a first type or second type of boundary condition?
Q.2
If solution does exist, how to solve it numerically?
- I tried to write in differential equation in matrix format, then apply Newton method. It is very difficult to have a converge scheme.
A more detailed simple example is attached to explain the solution that I tried.
Many thanks for your ideas or comments
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