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2.6. 1D Wave equation: IBVP-Visualization on the finite interval

For wave equation $$ u_{tt}-c^2u_{xx}=0\qquad \text{as } 0<x<L $$ we consider reflection of the wave from the boundary at $x=0$ and $x=L$

under Dirichlet boundary condition on both ends $u|_{x=0}=u|_{x=L}=0$;

under Neumann boundary condition on both ends $u_x|_{x=0}=u_x|_{x=L}=0$;

under Dirichlet boundary condition on the left end and Neumann boundary condition on the right end $u|_{x=0}=u_x|_{x=L}=0$.