A FAST SOLVER FOR THE BACKWARD HEAT CONDUCTION PROBLEM IN UNBOUNDED DOMAINS - Theoretical and Computational Research in the 21st Century - page 84

The numerical solution obtained with N = 33 is displayed on Figures
(3.4) and (3.5). Here, we take the planes z = 0.0 and z = 0.7, respectively.
The resulting errors are E 0.0 = E 0.77 =10 −7 .
FIGURE 3.4 Numerical approximation of Eq. (14), obtained by Eq. (9) for the final
function (13) at t = 500 s with N = 33. The values of u ( x 1 , x 2 ,0, 500) and the corresponding
approximated values u q (0) are given on the vertical axes of the left-hand and right-hand
side figures, respectively. The error for this case is 10−7.
FIGURE 3.5 Numerical approximation of Eq. (14), obtained by Eq. (9) for the final
function (13) at t = 500 s with N = 33. The values of u ( x 1 , x 2 , 0.7, 500) and the corresponding
approximated values u q (0) are given on the vertical axes of the left-hand and right-hand
side figures, respectively. The error for this case is 10−7.