Learn more about 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 u_tt - cΔu = 0 are waves moving with speed .

Using a given triangulation of Ω, 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

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

The Parabolic Equation

The Eigenvalue Equation

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