Consider the problem ut =kuxx for 0 < x < l, with the
Chapter 5, Problem 5.3.4(choose chapter or problem)
Consider the problem ut =kuxx for 0 < x < l, with the boundary conditions u(0,t)=U, ux(l,t)=0, and the initial condition u(x,0)=0, where U is a constant. (a) Find the solution in series form. (Hint: Consider u(x,t)U.) (b) Using a direct argument, show that the series converges for t > 0. (c) If is a given margin of error, estimate how long a time is required for the value u(l, t) at the endpoint to be approximated by the constantU withintheerror .(Hint:Itisanalternatingserieswithrst term U, so that the error is less than the next term.)
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