little_ja-o
New member
- Joined
- Jun 30, 2006
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Assume a solution of the form u(x, t) = X(x)T(t) to the modified diffusion
equation ut − Duxx − u = 0. First show that the equation separates and
find the general solution for X(x) and T(t). Next, assuming that D > 0, >= 0, L > 0, solve the boundary value problem
ut − Duxx − u = 0 for all 0 <= x <= L, t >= 0
u(0, t) = u(L, t) = 0, for all t >= 0 (1)
u(x, 0) = sin((pi)x/L) + sin(2(pi)x/L).
Finally characterise the difference between the solutions for > D(pi)^2/L^2 and
< D(pi)^2/L^2.
equation ut − Duxx − u = 0. First show that the equation separates and
find the general solution for X(x) and T(t). Next, assuming that D > 0, >= 0, L > 0, solve the boundary value problem
ut − Duxx − u = 0 for all 0 <= x <= L, t >= 0
u(0, t) = u(L, t) = 0, for all t >= 0 (1)
u(x, 0) = sin((pi)x/L) + sin(2(pi)x/L).
Finally characterise the difference between the solutions for > D(pi)^2/L^2 and
< D(pi)^2/L^2.