[Fishy]

Is this equation hyperbolic or elliptic?

F=[(∂^2 u)/∂x^2] - u

[FMDenaro]

Originally Posted by Fishy

Is this equation hyperbolic or elliptic?

F=[(∂^2 u)/∂x^2] - u

First, that appears as a second order ODE, not a PDE. However, you can determine the eigenvalues to determine the mathematical character of the equation.

[aero_head]

Hello,

The equation you gave us is a second order ordinary differential equations (ODE). From the definition, ODE's contain differentials with respect to only one variable, whereas partial differential equations (PDE's) contain differentials with respect to more than one independent variable.

Other than determining the eigenvalues as stated above from the PDE, you can also tell if it is parabolic or hyperbolic from the characteristics of the flow associated with the equation. For example, diffusion processes are associated with parabolic PDE's.

[duri]

Originally Posted by Fishy

Is this equation hyperbolic or elliptic?

F=[(∂^2 u)/∂x^2] - u

Is this 1D version of PDE? If so, then the equation is elliptic, this is Poisson's equation with source term same as solution variable.
Otherwise as mentioned in other replies it is second order ODE. Solution to the problem can be found in text books. In this case there is no elliptic or hyperbolic concept.