Find the finite-difference solution of the heat-conduction
problem
PDE: ut = uxx 0 < x < 1, 0 < t < 1
BCs:
⇢
u(0, t) = 0
ux(1, t) = 0
0 < t < 1
IC: u(x, 0) = sin(pi x) 0 x 1
for t = 0.005, 0.010, 0.015 by the explicit method. Assume
Consider the nonhomogenous heat equation with time dependent
sources ut = uxx + xt, an initial condition
u(x, 0) = x2 and inhomogenous boundary conditions
ux(0, t) = 2t and ux(1, t) = 4. Use eigen
function expansion to find the solution u(x, t).
Classify the following system with output current given (by the
equation below) as linear/non linear
i0(t)= 5 i1(t) + 8 i2 (t-10) + 0.25 i3 (t+2)
Is this linear or non linear