Partial Differential Equation Toolbox |

The Hyperbolic Equation

Using the same ideas as for the parabolic equation, `hyperbolic` implements the numerical solution of

with the initial conditions

and usual boundary conditions. In particular, solutions of the equation
utt - cu = 0 are waves moving with speed .

Using a given triangulation of , the method of lines yields the second order ODE system

with the initial conditions

after we eliminate the unknowns fixed by Dirichlet boundary conditions. As before, the stiffness matrix K and the mass matrix M are assembled with the aid of the function `assempde` from the problems

- · (cu) + au = f and - · (0u) + du = 0

| Solving the Parabolic Equation in Stages |  | The Eigenvalue Equation |