Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Solve hyperbolic PDE problem

Hyperbolic equation solver

Solves PDE problems of the type

$$d\frac{{\partial}^{2}u}{\partial {t}^{2}}-\nabla \cdot \left(c\nabla u\right)+au=f$$

on a 2-D or 3-D region Ω, or the system PDE problem

$$d\frac{{\partial}^{2}u}{\partial {t}^{2}}-\nabla \cdot \left(c\otimes \nabla u\right)+au=f$$

The variables *c*, *a*, *f*,
and *d* can depend on position, time, and the solution *u* and
its gradient.

`hyperbolic`

is not recommended. Use `solvepde`

instead.

- example
`u = hyperbolic(u0,ut0,tlist,model,c,a,f,d)`

- example
`u = hyperbolic(u0,ut0,tlist,b,p,e,t,c,a,f,d)`

- example
`u = hyperbolic(u0,ut0,tlist,Kc,Fc,B,ud,M)`

`u = hyperbolic(___,rtol)`

`u = hyperbolic(___,rtol,atol)`

- example
`u = hyperbolic(u0,ut0,tlist,Kc,Fc,B,ud,M,___,'DampingMatrix',D)`

`u = hyperbolic(___,'Stats','off')`

produces
the solution to the FEM formulation of the scalar PDE problem`u`

= hyperbolic(`u0`

,`ut0`

,`tlist`

,`model`

,`c`

,`a`

,`f`

,`d`

)

$$d\frac{{\partial}^{2}u}{\partial {t}^{2}}-\nabla \cdot \left(c\nabla u\right)+au=f$$

on a 2-D or 3-D region Ω, or the system PDE problem

$$d\frac{{\partial}^{2}u}{\partial {t}^{2}}-\nabla \cdot \left(c\otimes \nabla u\right)+au=f$$

with geometry, mesh, and boundary conditions specified in `model`

,
with initial value `u0`

and initial derivative with
respect to time `ut0`

. The variables *c*, *a*, *f*,
and *d* in the equation correspond to the function
coefficients `c`

, `a`

, `f`

,
and `d`

respectively.

turns
off the display of internal ODE solver statistics during the solution
process.`u`

= hyperbolic(___,'Stats','off')

Was this topic helpful?