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Finite approximation of PDEs

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Homework Statement


Given u_tt = F(x,t,u,u_x, u_xx), give the finite difference approximation of the pde (ie using u_x = (u(x + dx; t) - u(x - dx; t))/(2dx) etc.)


Homework Equations


Well, clearly, u_x = (u(x + dx; t) - u(x - dx; t))/(2dx)


The Attempt at a Solution


I really have no idea how that formula applies, but I do know that u_tt = u(x,t+dt) - 2u(x,t) + u(x,t-dt) / 2(dt)^2. How the non-homogeneous term F applies, I have no clue.


I'd be eternally grateful for any help anyone has to provide....considering I was the only person to reply to my last thread (on PDEs.)
 

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