# PDE Problem

A pde problem combines a partial differential equation (pde), an initial boundary condition and boundary conditions.

## Codebook

### Construction

Assume the following initial value/boundary problem is to be instantiated:

$\displaystyle{ u_{t}(x,t) = \frac{1}{2}u_{xx}(x,t) }$

s.t.

$\displaystyle{ u(x,0) = \sin(x) ,~ 0 \leq x \leq 1, }$

$\displaystyle{ u(0,t) = 0 }$

$\displaystyle{ u(1,t) = 0 }$