Use the Forward-Difference method to approximate the solution to the following parabolic partial differential equations. 3u . 3 2 u a. -t=0, 0 < x < 4, 0 < f; 3t 71 rix2 h(0, t) m(4, r) = 0, 0 < r, h(x. 0) = sin |x (l + 2 cos |x), 0 < x < 4. Use h 0.2 and k 0.04 and compare your results at / = 0.4 to the actual solution u(x, t) e~' sin fx + c _ ' /4 sin fx. du 1 d 2 u b - lu 2 TT = 0 ' 0 < x < 1, 0 < t; dt 7T dx2 m(0, /) = m(I, f) = 0, 0 < r, i/(x, 0) = COSTT (x 5) , 0

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