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1D wave PDE with extended periodic IC 
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#1
Oct605, 11:21 AM

P: 45

I have formula for 1D wave equation:
(*) u(x, t) = 1/2 [ f(x + ct) + f(x  ct) ] + 1 / (2c) Integral( g(s), wrt s, from xct to x+ct ) I am trying to find u(1/2, 3/2) when L = 1, c = 1, f(x) = 0, g(x) = x(1  x). However, for (*) to work, the initial position f(x) and initial velocity g(x) must be extended to periodic functions. "To determine f(x) and g(x) we need only find the integer n s.t. nL <= x < (n+1)L, [where L is the right boundary length from the origin]." It then gives the ways of extending if n is even or odd. If even, gx) = g(x  nL). If odd, g(x) = g((n+1)L  x). How do I determine what n is for g to extend it correctly? I need to figure out nL <= x < (n+1)L, yes. But what is x for g? For f(x+ct) it is clear. But g is in the integral... 


#2
Oct605, 06:48 PM

P: 1,440

did you take your question from 'A First Course in Partial Differential Equations with complex variables and transform methods' by H F Weinberger?
anyway here is that question i had posted earlier http://physicsforums.com/showthread.php?t=90027 


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