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Interpolate numerical solution of PDE

`[`

interpolates a numerical solution returned by `u`

,`dudx`

] = pdeval(`m`

,`xmesh`

,`usol`

,`xq`

)`pdepe`

at new query points
`xq`

, and returns the interpolated values of the solution
`u`

and their partial derivative `dudx`

. The
`m`

, `xmesh`

, and `usol`

arguments are
reused from a previous call to `pdepe`

:

The numerical solution produced by

`sol = pdepe(m,@pdefun,@pdeic,@pdebc,xmesh,tspan)`

uses the coordinate symmetry`m`

and spatial mesh`xmesh`

to return a 3-D matrix of the solution values`sol`

. Reuse the`m`

and`xmesh`

inputs used to calculate the solution when you call`pdeval`

.The input vector

`usol = sol(i,:,k)`

is the value of component`k`

of the solution at time`tspan(i)`

. When there is only one solution component,`usol`

is a row extracted from the solution matrix`usol = sol(i,:)`

.

`pdeval`

evaluates the partial derivative $$\frac{\partial u}{\partial x}$$ rather than the flux $$f\left(x,t,u,\frac{\partial u}{\partial x}\right)$$. Although the flux is continuous, the partial derivative can have a jump at a material interface.