Partial Differential Equation Toolbox

Handling Boundary Conditions

The following boundary conditions can be handled for scalar u:

  • Dirichlet:
PD Equation Dirichlet Image
on the boundary
PD Equation dOmega Image
  • Generalized Neumann:
PD Equation Neumann Image
on
PD Equation dOmega Image
where
PD Equation N Image
is the outward unit normal and g, q, h, and r can be complex valued functions of x and y defined on
PD Equation dOmega Image
. For the nonlinear PDE, the coefficients may depend on u. For time-dependent problems, the coefficients may also depend on t. For PDE systems, Dirichlet, generalized Neumann, and mixed boundary conditions are supported.
Partial Differential Equation Toolbox Visualizations Tools Image

Visualization tools provide multiple ways to plot results. A contour plot with gradient arrows shows the temperature and heat flux. The temperature gradient is displayed using 3-D plotting tools.

Next: Toolbox Application Modes

Try Partial Differential Equation Toolbox

Get trial software

Free Partial Differential Equation Toolbox Technical Kit

Get the kit now