Numerical Analysis, Eighth Edition

by Richard L. Burden and J. Douglas Faires

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Heat Equation Backward-Difference Method

To approximate the solution of the Parabolic partial-differential equation subject to the boundary conditions  u(0,t) = u(l,t) = 0, 0<= t <= T= max t,  and the conditions: u(x,0) = F( x), 0 <= x <= 1.