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(Not recommended) 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.

`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*, *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')

`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.

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