The one-dimensional wave equation is represented by the following mathematical model: ∂^u/∂t^2= c^2 ∂^u/∂x^2 xЄ (0,L), tЄ (0,T] u(x,0) = l(x) xЄ (0,L) ∂/∂t u(x,0) = 0 xЄ (0,L)
u(0,t) = 0 tЄ (0,T] u(L,t) = 0 tЄ (0,T] The above PDE describes the vibration of string fixed at both ends. u(x,t) is the displacement, which varies in space and time. I(x) is the initial shape of the string. Use an appropriate finite difference scheme to discretize the above equations considering a uniform mesh of spacings Ax and At. Draw the stencil and formulate the finite difference approximation to solve the PDE.