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*,

`hyperbolic`

is not recommended. Use `solvepde`

instead.

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

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

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

`u = hyperbolic(___,rtol)`

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

`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*,

`c`

, `a`

, `f`

,
and `d`

respectively.

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

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

`hyperbolic`

internally calls `assema`

, `assemb`

,
and `assempde`

to create finite element matrices
corresponding to the problem. It calls `ode15s`

to
solve the resulting system of ordinary differential equations. For
details, see Hyperbolic Equations.

Was this topic helpful?