Heat equation with Robin boundary conditions
Consider the heat equation of the form ?u ?t = ?2u ?x2, with Robin boundary conditions ?u ?x(0,t) = ?1,u(L,t) = 0, where L = 2?, and initial conditon u(x,0) = f(x). Write a forward difference scheme to solve this equation. Consider initial con- ditions of the form f(x) = 2? ?x + Asin x where A = 2,4,···,10. Obtain the solution after a sufficiently long time (e.g. T = 50). Analyze the solution at the termination time, and try to predict the steady-state solution of the equation.k=0.01 and N = 200
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