Let us be given the following initial BVP uu(x,t) = 4 u(x, t) u(0,t) = u(30,t)...

 

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Let us be given the following initial BVP uu(x,t) = 4 u(x, t) u(0,t) = u(30,t) = 0 u(x, 0) = f(x) 0<r<30, t>0; t>0; 0 < x <30; 0 < x < 30. Here (x, 0) = 0 f(x)= )= {(30-r)/20 0≤x≤ 10; (30-x)/2010 < x ≤ 30. (4) (5) 1. Extend the function f to an odd function on the interval [-30, 30]. Denote this new function h. Then, extend h to a periodic function of period 60. 2. Solve the IVP by using separation of variables. Let us be given the following initial BVP uu(x,t) = 4 u(x, t) u(0,t) = u(30,t) = 0 u(x, 0) = f(x) 0<r<30, t>0; t>0; 0 < x <30; 0 < x < 30. Here (x, 0) = 0 f(x)= )= {(30-r)/20 0≤x≤ 10; (30-x)/2010 < x ≤ 30. (4) (5) 1. Extend the function f to an odd function on the interval [-30, 30]. Denote this new function h. Then, extend h to a periodic function of period 60. 2. Solve the IVP by using separation of variables.