Given an initial-boundary value problem for the heat equation 1 00 16 u(0,1) = u(1,t) = 0, t20 u(x,0) = 2sin(2nx) with step size At = 0.01 and Ar=0.2. By using finite difference formula, find the equation of u;, 1 . a) b) Sketch a stencil in (x, t) plane, based on the u,obtained in (a). c) Then, find all the solutions of the initial-boundary value problem up to t = 0.01. (Show your calculations in detail).

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